opinion: Justice Kagan
  delivered the opinion of the Court.
  In this case, a Federal District Court enjoined a state court from considering a plaintiff’s request to approve a class action. The District Court did so because it had earlier denied a motion to certify a class in a related case, brought by a different plaintiff against the same defendant alleging similar claims. The federal court thought its injunction appropriate to prevent relitigation of the issue it had decided.
  We hold to the contrary. In issuing this order to a state court, the federal court exceeded its authority under the “relitigation exception” to the Anti-Injunction Act. That statutory provision permits a federal court to enjoin a state proceeding only in rare cases, when necessary to “protect or effectuate [the federal court’s] judgments.” 28 U. S. C. §2283. Here, that standard was not met for two reasons. First, the issue presented in the state court was not identical to the one decided in the federal tribunal. And second, the plaintiff in the state court did not have the requisite connection to the federal suit to be bound by the District Court’s judgment.
  I
  Because the question before us involves the effect of a former adjudication on this case, we begin our statement of the facts not with this lawsuit, but with another. In August 2001, George McCollins sued respondent Bayer Corporation in the Circuit Court of Cabell County, West Virginia, asserting various state-law claims arising from Bayer’s sale of an allegedly hazardous prescription drug called Baycol (which Bayer withdrew from the market that same month). McCol-lins contended that Bayer had violated West Virginia’s consumer protection statute and the company’s express and implied warranties by selling him a defective product. And pursuant to West Virginia Rule of Civil Procedure 23 (2011), MeCollins asked the state court to certify a class of West Virginia residents who had also purchased Baycol, so that the case could proceed as á class action.
  Approximately one month later, the suit now before us began in a different part of West Virginia. Petitioners Keith Smith and Shirley Sperlazza (Smith for short) filed state-law claims against Bayer, similar to those raised in MeCollins’ suit, in the Circuit Court of Brooke County, West Virginia. And like MeCollins, Smith asked the court to certify under West Virginia’s Rule 23 a class of Baycol purchasers residing in the State. Neither Smith nor MeCollins knew about the other’s suit.
  In January 2002, Bayer removed MeCollins’ case to the United States District Court for the Southern District of West Virginia on the basis of diversity jurisdiction. See 28 U. S. C. §§ 1332, 1441. The case was then transferred to the District of Minnesota pursuant to a preexisting order of the Judicial Panel on Multi-District Litigation, which had consolidated all federal suits involving Baycol (numbering in the tens of thousands) before a single District Court Judge. See §1407. Bayer, however, could not remove Smith’s case to federal court because Smith had sued several West Virginia defendants in addition to Bayer, and so the suit lacked complete diversity. See § 1441(b). Smith’s suit thus remained in the state courthouse in Brooke County.
  Over the next six years, the two cases proceeded along their separate pretrial paths at roughly the same pace. By 2008, both courts were preparing to turn to their respective plaintiffs’ motions for class certification. The Federal District Court was the first to reach a decision.
  Applying Federal Rule of Civil Procedure 23, the District Court declined to certify McCollins’ proposed class of West Virginia Baycol purchasers. The District Court’s reasoning proceeded in two steps. The court first ruled that, under West Virginia law, each plaintiff would have to prove “actual injury” from his use of Baycol to recover. App. to Pet. for Cert. 44a. The court then held that because the necessary showing of harm would vary from plaintiff to plaintiff, “individual issues of fact predominate^]” over issues common to all members of the proposed class, and so the case was not suitable for class treatment. Id., at 45a. In the same order, the District Court also dismissed McCollins’ claims on the merits in light of his failure to demonstrate physical injury from his use of Baycol. McCollins chose not to appeal.
  Although McCollins’ suit was now concluded, Bayer asked the District Court for another order based upon it, this one affecting Smith’s case in West Virginia. In a motion — receipt of which first apprised Smith of McCollins’ suit — Bayer explained that the proposed class in Smith’s ease was identical to the one the federal court had just rejected. Bayer therefore requested that the federal court enjoin the West Virginia state court from hearing Smith’s motion to certify a class. According to Bayer, that order was appropriate to protect the District Court’s judgment in McCollins’ suit denying class certification. The District Court agreed and granted the injunction.
  The Court of Appeals for the Eighth Circuit affirmed. In re Baycol Prods. Litigation, 593 F. 3d 716 (2010). The court noted that the Anti-Injunction Act generally prohibits federal courts from enjoining state court proceedings. But the court held that the Act’s relitigation exception authorized the injunction here because ordinary rules of issue preclusion barred Smith from seeking certification of his proposed class. According to the court, Smith was invoking a similar class action rule as McCollins had used to seek certification “of the same class” in a stdt alleging “the same legal theories,” id., at 724; the issue in the state court therefore was “sufficiently identical” to the one the federal court had decided to warrant preclusion, ibid. In addition, the court held, the parties in the two proceedings were sufficiently alike: Because Smith was an unnamed member of the class McCollins had proposed, and because their “interests were aligned,” Smith was appropriately bound by the federal court’s judgment. Ibid.
  We granted certiorari, 561 U. S. 1057 (2010), because the order issued here implicates two circuit splits arising from application of the Anti-Injunction Act’s relitigation exception. The first involves the requirement of preclusion law that a subsequent suit raise the “same issue” as a previous case. The second concerns the scope of the rule that a court’s judgment cannot bind nonparties. We think the District Court erred on both grounds when it granted the injunction, and we now reverse.
  HH HH
  The Anti-Injunction Act, first enacted in 1793, provides:
  “A court of the United States may not grant an injunction to stay proceedings in a State court except as expressly authorized by Act of Congress, or where necessary in aid of its jurisdiction, or to protect or effectuate its judgments.” 28 U. S. C. § 2283.
  The statute, we have recognized, “is a necessary concomitant of the Framers' decision to authorize, and Congress’ decision to implement, a dual system of federal and state courts.” Chick Kam Choo v. Exxon Corp., 486 U. S. 140, 146 (1988). And the Act’s core message is one of respect for state courts. The Act broadly commands that those tribunals “shall remain free from interference by federal courts.” Atlantic Coast Line R. Co. v. Locomotive Engineers, 398 U. S. 281, 282 (1970). That edict is subject to only “three specifically defined exceptions.” Id., at 286. And those exceptions, though designed for important purposes, “are narrow and are ‘not [to] be enlarged by loose statutory construction.’” Chick Kam Choo, 486 U. S., at 146 (quoting Atlantic Coast Line, 398 U. S., at 287; alteration in original). Indeed, “[a]ny doubts as to the propriety of a federal injunction against state court proceedings should be resolved in favor of permitting the state courts to proceed.” Id., at 297.
  This case involves the last of the Act’s three exceptions, known as the relitigation exception. That exception is designed to implement “well-recognized concepts” of claim and issue preclusion. Chick Kam Choo, 486 U. S., at 147. The provision authorizes an injunction to prevent state litigation of a claim or issue “that previously was presented to and decided by the federal court.” Ibid. But in applying this exception, we have taken special care to keep it “strict and narrow.” Id., at 148. After all, a court does not usually “get to dictate to other courts the preclusion consequences of its own judgment.” 18 C. Wright, A. Miller, & E. Cooper, Federal Practice and Procedure §4405, p. 82 (2d ed. 2002) (hereinafter Wright & Miller): ■ Deciding whether and how prior litigation has preclusive effect is usually the bailiwick of the second court (here, the one in West Virginia). So issuing an injunction under the relitigation exception is resorting to heavy artillery. For that reason, every benefit of the doubt goes toward the state court, see Atlantic Coast Line, 398 U. S., at 287, 297; an injunction can issue only if preclusion is clear beyond peradventure.
  The question here is whether the federal court’s rejection of McCollins’ proposed class precluded a later adjudication in state court of Smith’s certification motion. For the federal court’s determination of the class issue to have this preclu-sive effect, at least two conditions must be met. First, the issue the federal court decided must be the same as the one presented in the state tribunal. See 18 Wright & Miller § 4417, at 412. And second, Smith must have been a party to the federal suit, or else must fall within one of a few discrete exceptions to the general rule against binding nonparties. See 18A id., § 4449, at 330. In fact, as we will explain, the issues before the two courts were not the same, and Smith was neither a party nor the exceptional kind of nonparty who can be bound. So the courts below erred in finding the certification issue precluded, and erred all the more in thinking an injunction appropriate.
  A
  In our most recent case on the relitigation exception, Chick Kam Choo v. Exxon, we applied the “same issue” requirement of preclusion law to invalidate a federal court’s injunction. 486 U. S., at 151. The federal court had dismissed a suit involving Singapore law on grounds of forum non conveniens. After the plaintiff brought the same claim in Texas state court, the federal court issued an injunction barring the plaintiff from pursuing relief in that alternate forum. We held that the District Court had gone too far. “[A]n essential prerequisite for applying the relitigation exception,” we explained, “is that the . . . issues which the federal injunction insulates from litigation in state proceedings actually have been decided by the federal court.” Id., at 148. That prerequisite, we thought, was not satisfied because the issue to be adjudicated in state court was not the one the federal court had resolved. The federal court had considered the permissibility of the claim under federal forum non conveniens principles. But the Texas courts, we thought, “would apply a significantly different forum non conveniens analysis,” id., at 149; they had in prior cases rejected the strictness of the federal doctrine. Our conclusion followed: “[W]hether the Texas state courts are an appropriate forum for [the plaintiff’s] Singapore law claims has not yet been litigated.” Ibid. Because the legal standards in the two courts differed, the issues before the courts differed, and an injunction was unwarranted.
  The question here closely resembles the one in Chick Kam Choo. The class Smith proposed in state court mirrored the class McCollins sought to certify in federal court: Both included all Baycol purchasers resident in West Virginia. Moreover, the substantive claims in the two suits broadly overlapped: Both complaints alleged that Bayer had sold a defective product in violation of the State’s consumer protection law and the company’s warranties. So far, so good for preclusion. But not so fast: a critical question — the question of the applicable legal standard — remains. The District Court ruled that the proposed class did not meet the requirements of Federal Rule 23 (because individualized issues would predominate over common ones). But the state court was poised to consider whether the proposed class satisfied West Virginia Rule 23. If those two legal standards differ (as federal and state forum non conveniens law differed in Chick Kam Choo) — then the federal court resolved an issue not before the state court. In that event, much like in Chick Kam Choo, “whether the [West "Virginia] state cour[t]” should certify the proposed class action “has not yet been litigated.” 486 U. S., at 149.
  The Court of Appeals and Smith offer us two competing ways of deciding whether the West Virginia and Federal Rules differ, but we think the right path lies somewhere in the middle. The Eighth Circuit relied almost exclusively on the near-identity of the two Rules’ texts. See 593 F. 3d, at 723. That was the right place to start, but not to end. Federal and state courts, after all, can and do apply identically worded procedural provisions in widely varying ways. If a State’s procedural provision tracks the language of a Federal Rule, but a state court interprets that provision in a manner federal courts have not, then the state court is using a different standard and thus deciding a different issue. See 18 Wright & Miller § 4417, at 454 (stating that preclusion is “inappropriate” when “different legal standards . . . masquer-ad[e] behind similar legal labels”). At the other extreme, Smith contends that the source of law is all that matters: a different sovereign must in each and every case “ ‘have the opportunity, if it chooses, to construe its procedural rule differently/ ” Brief for Petitioners 22 (quoting ALI, Principles of the Law, Aggregate Litigation §2.11, Reporters’ Notes, Comment b, p. 179 (2010)). But if state courts have made crystal clear that they follow the same approach as the federal court applied, we see no need to ignore that determination; in that event, the issues in the two cases would indeed be the same. So a federal court considering whether the relitigation exception applies should examine whether state law parallels its federal counterpart. But as suggested earlier, see supra, at 307, the federal court must resolve any uncertainty on that score by leaving the question of preclusion to the state courts.
  Under this approach, the West Virginia Supreme Court has gone some way toward resolving the matter before us by declaring its independence from federal courts’ interpretation of the Federal Rules — and particularly of Rule 23. In In re W Va. Rezulin Litigation, 214 W. Va. 52, 585 S. E. 2d 52 (2003) (In re Rezulin), the West Virginia high court considered a plaintiff’s motion to certify a class — coincidentally enough, in a suit about an allegedly defective pharmaceutical product. The court made a point of complaining about the parties’ and lower court’s near-exclusive reliance on federal cases about Federal Rule 23 to decide the certification question. Such cases, the court cautioned, “ ‘may be persuasive, but [they are] not binding or controlling.’” Id., at 61, 585 S. E. 2d, at 61. And lest anyone mistake the import of this message, the court went on: The aim of “this rule is to avoid having our legal analysis of our Rules ‘amount to nothing more than Pavlovian responses to federal decisional law.’ ” Ibid, (emphasis deleted). Of course, the state courts might still have adopted an approach to their Rule 23 that tracked the analysis the federal court used in McCollins’ case. But absent clear evidence that the state courts had done so, we could not conclude that they would interpret their Rule in the same way. And if that is so, we could not tell whether the certification issues in the state and federal courts were the same. That uncertainty would preclude an injunction.
  But here the case against an injunction is even stronger, because the West Virginia Supreme Court has disapproved the approach to Rule 23(b)(3)’s predominance requirement that the Federal District Court embraced. Recall that the federal court held that the presence of a single individualized issue — injury from the use of Baycol — prevented class certification. See supra, at 304. The court did not identify the common issues in the case; nor did it balance these common issues against the need to prove individual injury to determine which predominated. The court instead applied a strict test barring class treatment when proof of each plaintiff’s injury is necessary. By contrast, the West Virginia Supreme Court in In re Rezulin adopted an all-things-considered, balancing inquiry in interpreting its Rule 23. Rejecting any “rigid test,’’ the state court opined that the predominance requirement “contemplates a review of many factors.” 214 W. Va., at 72, 585 S. E. 2d, at 72. Indeed, the court noted, a “ ‘single common issue’ ” in a case could outweigh “‘numerous . . . individual questions.’” Ibid. That meant, the court further explained (quoting what it termed the “leading treatise” on the subject), that even objections to certification “ ‘based on ... causation, or reliance’ ” — which typically involve showings of individual injury — “‘will not bar predominance satisfaction.’” Ibid, (quoting 2 A. Conte & H. Newberg, Newberg on Class Actions §4.26, p. 241 (4th ed. 2002)). So point for point, the analysis set out in In re Rezulin diverged from the District Court’s interpretation of Federal Rule 23. A state court using the In re Rezulin standard would decide a different question than the one the federal court had earlier resolved.
  This case, indeed, is little more than a rerun of Chick Earn Choo. A federal court and a state court apply different law. That means they decide distinct questions. The federal court’s resolution of one issue does not preclude the state court’s determination of another. It then goes without saying that the federal court may not issue an injunction. The AwA-Injunetion Act’s re-litigation exception does not extend nearly so far.
  B
  The injunction issued here runs into another basic premise of preclusion law: A court’s judgment binds only the parties to a suit, subject to a handful of discrete and limited exceptions. See, e.g., 18A Wright & Miller .§4449, at 330. The importance of this rule and the narrowness of its exceptions go hand in hand. We have repeatedly “emphasize[d] the fundamental nature of the general rule” that only parties can be bound by prior judgments; accordingly, we have taken a “constrained approach to nonparty preclusion.” Taylor v. Sturgell, 553 U. S. 880, 898 (2008). Against this backdrop, Bayer defends the decision below by arguing that Smith— an unnamed member of a proposed but uncertified class— qualifies as a party to the McCollins litigation. See Brief for Respondent 32-34. Alternatively, Bayer claims that the District Court’s judgment binds Smith under the recognized exception to the rule against nonparty preclusion for members of class actions. See id., at 34-39. We think neither contention has merit.
  Bayer’s first claim ill-comports with any proper understanding of what a “party” is. In general, “[a] ‘party* to litigation is ‘[o]ne by or against whom a lawsuit is brought,’” United States ex rel. Eisenstein v. City of New York, 556 U. S. 928, 933 (2009), or one who “become[s] a party by intervention, substitution, or third-party practice,” Karcher v. May, 484 U. S. 72, 77 (1987). And we have further held that an unnamed member of a certified class may be “considered a ‘party’ for the [particular] purpos[e] of appealing” an adverse judgment. Devlin v. Scardelletti, 536 U. S. 1, 7 (2002). But as the dissent in Devlin noted, no one in that case was “willing to advance the novel and surely erroneous argument that a nonnamed class member is a party to the class-action litigation before the class is certified.” Id., at 16, n. 1 (opinion of Scalia, J.). Still less does that argument make sense once certification is denied. The definition of the term “party” can on no account be stretched so far as to cover a person like Smith, whom the plaintiff in a lawsuit was denied leave to represent. If the judgment in the McCollins litigation can indeed bind Smith, it must do so under principles of non-party preclusion.
  As Bayer notes, see Brief for Respondent 37, one such principle allows unnamed members of a class action to be bound, even though they are not parties to the suit. See Cooper v. Federal Reserve Bank of Richmond, 467 U. S. 867, 874 (1984) (“[Ujnder elementary principles of prior adjudication a judgment in a properly entertained class action is binding on class members in any subsequent litigation”); see also Taylor, 553 U. S., at 894 (stating that nonparties can be bound in “properly conducted class actions”). But here Bayer faces a conundrum. If we know one thing about the McCollins suit, we know that it was not a class action. Indeed, the very ruling that Bayer argues ought to be given preclusive effect is the District Court’s decision that a class could not properly be certified. So Bayer wants to bind Smith as a member of a class action (because it is only as such that a nonparty in Smith’s situation can be bound) to a determination that there could not be a class action. And if the logic of that position is not immediately transparent, here is Bayer’s attempt to clarify: “[Ujntil the moment when class certification was denied, the McCollins case was a properly conducted class action.” Brief for Respondent 37. That is true, according to Bayer, because McCollins’’interests were aligned with the members of the class he proposed and he “act[ed] in a representative capacity when he sought class certification.” Id., at 36.
  But wishing does not make it so. McCollins sought class certification, but he failed to obtain that result. Because the District Court found that individual issues predominated, it held that the action did not satisfy Federal Rule 23’s requirements for class proceedings. In these circumstances, we cannot say that a properly conducted class action existed at any time in the litigation. Federal Rule 23 determines what is and is not a class action in federal court, where McCollins brought his suit. So in the absence of a certification under that Rule, the precondition for binding Smith was not met. Neither a proposed class action nor a rejected class action may bind nonparties. What does have this effect is a class action approved under Rule 23. But McCollins’ lawsuit was never that.
  We made essentially these same points in Taylor v. Stur-gell just a few Terms ago. The question there concerned the propriety of binding nonparties under a theory of “virtual representation” based on “identity of interests and some kind of relationship between parties and nonparties.” 553 U. S., at 901. We rejected the theory unanimously, explaining that it “would fiecogniz[e], in effect, a common-law kind of class action.’ ” Ibid. Such a device, we objected, would authorize preclusion “shorn of [Rule 23’s] procedural protections.” Ibid. Or as otherwise stated in the opinion: We could not allow “circumvent[ion]” of Rule 23’s protections through a “virtual representation doctrine that allowed courts to 'create de facto class actions at will.’ ” Ibid. We could hardly have been more clear that a “properly conducted class action,” with binding effect on nonparties, can come about in federal courts in just one way — through the procedure set out in Rule 23. Bayer attempts to distinguish Taylor by noting that the party in the prior litigation there did not propose a class action. But we do not see why that difference matters. Yes, McCollins wished to represent a class, and made a motion to that effect. But it did not come to pass. To allow McCollins7 suit to bind nonparties would be to adopt the very theory Taylor rejected.
  Bayer’s strongest argument comes not from established principles of preclusion, but instead from policy concerns relating to use of the class action device. Bayer warns that under our approach class counsel can repeatedly try to certify the same class “by the simple expedient of changing the named plaintiff in the caption of the complaint.” Brief for Respondent 47-48. And in this world of “serial relitigation of class certification,” Bayer contends, defendants “would be forced in effect to buy litigation peace by settling.” Id., at 2,12; see also In re Bridgestone/Firestone, Inc., Tires Prods. Liability Litigation, 333 F. 3d 763, 767 (CA7 2003) (objecting to “an asymmetric system in which class counsel can win but never lose” because of their ability to relitigate the issue of certification).
  But this form of argument flies in the face of the rule against nonparty preclusion. That rule perforce leads to re-litigation of many issues, as plaintiff after plaintiff after plaintiff (none precluded by the last judgment because none a party to the last suit) tries his hand at establishing some legal principle or obtaining some grant of relief. We confronted a similar policy concern in Taylor, which involved litigation brought under the Freedom of Information Act (FOIA). The Government there cautioned that unless we bound nonparties a “ ‘potentially limitless’ ” number of plaintiffs, perhaps coordinating with each other, could “mount a series of repetitive lawsuits” demanding the selfsame documents. 553 U. S., at 903. But we rejected this argument, even though the payoff in a single successful FOIA suit— disclosure of documents to the public — could “trum[p]” or “subsum[e]” all prior losses, just as a single successful class certification motion could do. In re Bridgestone/Firestone, 333 F. 3d, at 766, 767. As that response suggests, our legal system generally relies on principles of stare decisis and comity among courts to mitigate the sometimes substantial costs of similar litigation brought by different plaintiffs. We have not thought that the right approach (except in the discrete categories of cases we have recognized) lies in binding nonparties to a judgment.
  And to the extent class actions raise special problems of relitigation, Congress has provided a remedy that does not involve departing from the usual rules of preclusion. In the Class Action Fairness Act of 2005 (CAFA), 28 U. S. C. §§ 1332(d), 1453 (2006 ed. and Supp. Ill), Congress enabled defendants to remove to federal court any sizable class action involving minimal diversity of citizenship. Once removal takes place, Federal Rule 23 governs certification. And federal courts may consolidate multiple overlapping suits against a single defendant in one court (as the Judicial Panel on Multi-District Litigation did for the many actions involving Baycol). See § 1407. Finally, we would expect federal courts to apply principles of comity to each other’s class certification decisions when addressing a common dispute. See, e. g., Cortez Byrd Chips, Inc. v. Bill Harbert Constr. Co., 529 U. S. 193, 198 (2000) (citing Landis v. North American Co., 299 U. S. 248, 254 (1936)). CAFA may be cold comfort to Bayer with respect to suits like this one beginning before its enactment. But Congress’s decision to address the relitigation concerns associated with class actions through the mechanism of removal provides yet another reason for federal courts to adhere in this context to longstanding principles of preclusion. And once again, that is especially so when the federal court is deciding whether to go so far as to enjoin a state proceeding.
  * *
  The Anti-Injunction Act prohibits the order the District Court entered here. The Act's relitigation exception authorizes injunctions only when a former federal adjudication clearly precludes a state court decision. As we said more than 40 years ago, and have consistently maintained since that time, “[a]ny doubts . . . should be resolved in favor of permitting the state courts to proceed.” Atlantic Coast Line, 398 U. S., at 297. Under this approach, close cases have easy answers: The federal court should not issue an injunction, and the state court should decide the preclusion question. But this case does not even strike us as close. The issues in the federal and state lawsuits differed because the relevant legal standards differed. And the mere proposal of a class in the federal action could not bind persons who were not parties there. For these reasons, the judgment of the Court of Appeals is
  .Reversed.
  Justice Thomas joins Parts I and II-A of this opinion.
  The Class Action Fairness Act of 2005, 119 Stat. 4, which postdates and therefore does not govern this lawsuit, now enables a defendant to remove to federal court certain docs actions involving nondiveroo parties. See 28 U. S. C. §§ 1332(d), 1453(b); see also infra, at 317-318.
  Although McCollins had originally sought certification under W. Va. Rule of Civ. Proc. 23 (2011), federal procedural rules govern a case that has been removed to federal court. See Skady Grove Orthopedic Associates, P. A. v. Allstate Ins. Co., 559 U. S. 393 (2010).
  Compare In re Bay col Prods. Litigation, 593 F. 3d 716,723 (CA8 2010) (ease below) (holding that two eases involve the same iosuo when “[t]ho state and federal [elass] certification rules .. . are not significantly different”), with J. R. Clearwater Inc. v. Ashland Chemical Co., 93 F. 3d 176, 180 (CA5 1996) (holding that two caaes implicate different issues evon when “[the state rule] is modeled on . . . the Federal Rules” because a “[state] court might well exercise [its] discretion in a different manner”).
  Compare 593 F. 3d, at 724 (“[T]he denial of elass certification is binding on unnamed [putative] class members” because they are “in privity to [the parties] in the prior action”), mid In re Bridgestone/Firestone, Inc., Tiros Prods. Liability Litigation, 333 F. 3d 763, 768-769 (CA7 2003) (same), with In re Ford Motor Co., 471 F. 3d 1233, 1245 (CA11 2006) (holding that “[t]he denial of elass certification” prevents a court from “binding” anyone other than “the parties appearing before it”), and In re General Motors Corp. Pick-Up Truck Fuel Tank Prods. Liability Litigation, 134 F. 3d 133, 141 (CA3 1998) (holding that putative “class memboro aro not partios” and so cannot be bound by a court’s ruling when “there is no class pending”).
  That is especially so because an injunction is not the only way to correct a state trial court’s erroneous refusal to give preclusive effect to a federal judgment. As we have noted before, “the state appellate courts and ultimately this Court” can review and reverse such a ruling. Atlantic Coast Line R. Co. v. Locomotive Engineers, 398 U. S. 281, 287 (1970).
  We have held that federal common law governs the preclusive effect of a decision of a federal court sitting in diversity. See Semtek Int’l Inc. v. Lockheed Martin Corp., 531 U. S. 497, 508 (2001). Smith assumes that federal common law should here incorporate West Virginia’s preclusion law, see Brief for Petitioners 15-16, whereas Bayer favors looking only to federal rules of preclusion because of the federal interests at stake in this ease, see Brief for Respondent 18. We do not think the question matters here. Neither party identifies any way in which federal and state principles of preclusion law differ in any relevant respect. Nor have we found any such divergence. Compare, e. g., Montana v. United States, 440 U. S. 147, 153-154 (1979) (describing elements of issue preclusion), with State v. Miller, 194 W. Va. 3, 9, 459 S. E. 2d 114, 120 (1995) (same). We therefore need not decide whether, in general, federal common law ought to incorporate state law in situations such as this.
  Because we rest our decision on the Anti-Injunction Act and the principles of issue preclusion that inform it, we do not consider Smith’s argument, based on Phillips Petroleum Co. v. Shutts, 472 U. S. 797 (1985), that the District Court’s action violated the Due Process Clause.
  The District Court’s approach to the predominance inquiry is consistent with the approach employed by the Eighth Circuit. See In re St. Jude Medical, Inc., 522 F. 3d 836, 837-840 (2008) (holding that most commercial misrepresentation eases are “unsuitable for class treatment” because individual issues of reliance necessarily predominate). We express no opinion as to the correctness of this approach.
  Bayer argues that In re Rezulin does not preclude an injunction in this ease because the West Virginia court there decided that common issues predominated over individual ioouco of damages, not over individual issues of liability (as exist here). See Brief for Respondent 25-26. We think Bayer is right about this distinction, but wrong about its consequence. Our point is not that In re Rezulin dictates the answer to the class certification question here; the two eases are indeed too dissimilar for that to be true. The point instead is that In re Rezulin articulated a general approach to the predominance requirement that differs markedly from the one the federal court used. Minor variations in the application of what is in essence the same legal standard do not defeat preclusion; but where, as here, the State’s courts “would apply a significantly different... analysis,” Chick Kam Choo v. Exxon Corp., 486 U. S. 140, 149 (1988), the federal and state courts decide different issues.
  In support of its claim that Smith counts as a party, Bayer cites two cases in which we held that a putative member of an uncertified class may wait until after the court rules on the certification motion to file an individual claim or move to intervene in the suit. See Brief for Respondent 32-33 (citing United Airlines, Inc. v. McDonald, 432 U. S. 385 (1977); American Pipe & Constr. Co. v. Utah, 414 U. S. 538 (1974)). But these eases, which were specifically grounded in policies of judicial administration, demonstrate only that a person not a party to a class suit may receive certain benefits (such as the tolling of a limitations period) related to that proceeding. See id., at 553; McDonald, 432 U. S., at 394, n. 15. That result is consistent with a commonplace of preclusion law — that nonparties sometimes may benefit from, even though they cannot be bound by, former litigation. See Parklane Hosiery Co. v. Shore, 439 U. S. 322, 326-333 (1979); Blonder-Tongue Laboratories, Inc. v. University of Ill. Foundation, 402 U. S. 313 (1971).
  The great weight of scholarly authority — from the Restatement of Judgments to the American Law Institute to Wright and Miller — agrees that an uncertified class action cannot bind proposed class members. See Restatement (Second) of Judgments § 41(1), p. 393 (1980) (A nonparty may be bound only when his interests are adequately represented by “[t]he representative of a class of persons similarly situated, designated as such with the approval of the court”); ALI, Principles of the Law Aggregate Litigation §2.11, Reporters’ Notes, Comment b, p. 181 (2010) (“[N]one of [the exceptions to the rule against nonparty preclusion] extend generally to the situation of a would-be absent class member with respect to a denial of class certification”); 18A Wright & Miller §4456, at 457-458 (“[AJbsent certification there is no basis for precluding a nonparty” under the class action exception).
  By the same token, nothing in our holding today forecloses legislation to modify established principios of preclusion should Congress decide that CAFA does not sufficiently prevent rclitigation of class certification motions. Nor does this opinion at all address the permissibility of a change in. the Federal Rules of Civil Procedure pertaining to this question. Cf. n. 7, supra (declining to reach Smith’s due process claim).