opinion: Justice Powell
  delivered the opinion of the Court.
  The principal issue in this case is whether a federal district court lawfully may enjoin a plaintiff who has prevailed in a trial in state court from executing the judgment in its favor pending appeal of that judgment to a state appellate court.
  I
  Getty Oil Co. and appellant Pennzoil Co. negotiated an agreement under which Pennzoil was to purchase about three-sevenths of Getty’s outstanding shares for $110 a share. Appellee Texaco Inc. eventually purchased the shares for $128 a share. On February 8, 1984, Pennzoil filed a complaint against Texaco in the Harris County District Court, a state court located in Houston, Texas, the site of Pennzoil’s corporate headquarters. The complaint alleged that Texaco tortiously had induced Getty to breach a contract to sell its shares to Pennzoil; Pennzoil sought actual damages of $7.53 billion and punitive damages in the same amount. On November 19, 1985, a jury returned a verdict in favor of Pennzoil, finding actual damages of $7.53 billion and punitive damages of $3 billion. The parties anticipated that the judgment, including prejudgment interest, would exceed $11 billion.
  Although the parties disagree about the details, it was clear that the expected judgment would give Pennzoil significant rights under Texas law. By recording an abstract of a judgment in the real property records of any of the 254 counties in Texas, a judgment creditor can secure a lien on all of a judgment debtor’s real property located in that county. See Tex. Prop. Code Ann. §§52.001-52.006 (1984). If a judgment creditor wishes to have the judgment enforced by state officials so that it can take possession of any of the debtor’s assets, it may secure a writ of execution from the clerk of the court that issued the judgment. See Tex. Rule Civ. Proc. 627. Rule 627 provides that such a writ usually can be obtained “after the expiration of thirty days from the time a final judgment is signed.” But the judgment debtor “may-suspend the execution of the judgment by filing a good and sufficient bond to be approved by the clerk.” Rule 364(a). See Rule 368. For a money judgment, “the amount of the bond . . . shall be at least the amount of the judgment, interest, and costs.” Rule 364(b).
  Even before the trial court entered judgment, the jury’s verdict cast a serious cloud on Texaco’s financial situation. The amount of the bond required by Rule 364(b) would have been more than $13 billion. It is clear that Texaco would not have been able to post such a bond. Accordingly, “the business and financial community concluded that Pennzoil would be able, under the lien and bond provisions of Texas law, to commence enforcement of any judgment entered on the verdict before Texaco’s appeals had been resolved.” App. to Juris. Statement A87 (District Court’s Supplemental Finding of Fact 40, Jan. 10, 1986). The effects on Texaco were substantial: the price of its stock dropped markedly; it had difficulty obtaining credit; the rating of its bonds was lowered; and its trade creditors refused to sell it crude oil on customary terms. Id., at A90-A98 (District Court’s Supplemental Findings of Fact 49-70).
  Texaco did not argue to the trial court that the judgment, or execution of the judgment, conflicted with federal law. Rather, on December 10, 1985 — before the Texas court entered judgment — Texaco filed this action in the United States District Court for the Southern District of New York in White Plains, New York, the site of Texaco’s corporate headquarters. Texaco alleged that the Texas proceedings violated rights secured to Texaco by the Constitution and various federal statutes. It asked the District Court to enjoin Pennzoil from taking any action to enforce the judgment. Pennzoil’s response, and basic position, was that the District Court could not hear the case. First, it argued that the Anti-Injunction Act, 28 U. S. C. § 2283, barred issuance of an injunction. It further contended that the court should abstain under the doctrine of Younger v. Harris, 401 U. S. 37 (1971). Third, it argued that the suit was in effect an appeal from the Texas trial court and that the District Court had no jurisdiction under the principles of Rooker v. Fidelity Trust Co., 263 U. S. 413 (1923), and District of Columbia Court of Appeals v. Feldman, 460 U. S. 462 (1983).
  The District Court rejected all of these arguments. 626 F. Supp. 250 (1986). It found the Anti-Injunction Act inapplicable because Texaco’s complaint rested on 42 U. S. C. § 1983. See Mitchum v. Foster, 407 U. S. 225 (1972) (holding that §1983 falls within the exceptions to the Anti-Injunction Act). It found Younger abstention unwarranted because it did not believe issuance of an injunction would “interfere with a state official’s pursuit of a fundamental state interest.” 626 F. Supp., at 260. As to the Rooker-Feldman doctrine, the court noted only that it was not “attempting to sit as a final or intermediate appellate state court as to the merits of the Texas action.. . . Our only intention is to assure Texaco its constitutional right to raise claims that we view as having a good chance of success.” Id., at 254 (citation and footnote omitted).
  The District Court justified its decision to grant injunctive relief by evaluating the prospects of Texaco’s succeeding in its appeal in the Texas state courts. It considered the merits of the various challenges Texaco had made before the Texas Court of Appeals and concluded that these challenges “present generally fair grounds for litigation.” Ibid. It then evaluated the constitutionality of the Texas lien and bond requirements by applying the test articulated in Mathews v. Eldridge, 424 U. S. 319 (1976). It concluded that application of the lien and bond provisions effectively would deny Texaco a right to appeal. It thought that the private interests and the State’s interests favored protecting Texaco’s right to appeal. Relying on its view of the merits of the state-court appeal, the court found the risk of erroneous deprivation “quite severe.” 626 F. Supp., at 257. Finally, it viewed the administrative burden on the State as “slight.” Ibid. In light of these factors, the District Court concluded that Texaco’s constitutional claims had “a very clear probability of success.” Id., at 258. Accordingly, the court issued a preliminary injunction.
  On appeal, the Court of Appeals for the Second Circuit affirmed. 784 F. 2d 1133 (1986). It first addressed the Rooker-Feldman doctrine and rejected the portion of the District Court’s opinion that evaluated the merits of the state-court judgment. It held, however, that the doctrine did not completely bar the District Court’s jurisdiction. It concluded that the due process and equal protection claims, not presented by Texaco to the Texas courts, were within the District Court’s jurisdiction because they were not “‘inextricably intertwined’” with the state-court action. Id., at 1144 (quoting District of Columbia Court of Appeals v. Feldman, supra, at 483, n. 16).
  Next, the court considered whether Texaco had stated a claim under §1983. The question was whether Texaco’s complaint sought to redress action taken “under color of” state law, 42 U. S. C. § 1983. The court noted that “Pennzoil would have to act jointly with state agents by calling on state officials to attach and seize Texaco’s assets.” 784 F. 2d, at 1145. Relying on its reading of Lugar v. Edmondson Oil Co., 457 U. S. 922 (1982), the court concluded that the enjoined action would have been taken under color of state law, and thus that Texaco had stated a claim under § 1983. 784 F. 2d, at 1145-1147. Because § 1983 is an exception to the Anti-Injunction Act, see Mitchum v. Foster, supra, the court also found that the Anti-Injunction Act did not prevent the District Court from granting the relief sought by Texaco.
  Finally, the court held that abstention was unnecessary. First, it addressed Pullman abstention, see Railroad Comm’n of Texas v. Pullman Co., 312 U. S. 496 (1941). It rejected that ground of abstention, holding that “the mere possibility that the Texas courts would find Rule 364 [concerning the supersedeas bond requirements] unconstitutional as applied does not call for Pullman abstention.” 784 F. 2d, at 1149. Next, it rejected Younger abstention. It thought that “[t]he state interests, at stake in this proceeding differ in both kind and degree from those present in the six cases in which the Supreme Court held that Younger applied.” Ibid. Moreover, it thought that Texas had failed to “provide adequate procedures for adjudication of Texaco’s federal claims.” Id., at 1150. Turning to the merits, it agreed with the District Court that Texaco had established a likelihood of success on its constitutional claims and that the balance of hardships favored Texaco. Accordingly, it affirmed the grant of in-junctive relief.
  Pennzoil filed a jurisdictional statement in this Court. We noted probable jurisdiction under 28 U. S. C. § 1254(2). 477 U. S. 903 (1986). We reverse.
  II
  The courts below should have abstained under the principles of federalism enunciated in Younger v. Harris, 401 U. S. 37 (1971). Both the District Court and the Court of Appeals failed to recognize the significant interests harmed by their unprecedented intrusion into the Texas judicial system. Similarly, neither of those courts applied the appropriate standard in determining whether adequate relief was available in the Texas courts.
  A
  The first ground for the Younger decision was “the basic doctrine of equity jurisprudence that courts of equity should not act, and particularly should not act to restrain a criminal prosecution, when the moving party has an adequate remedy at law.” Id., at 43. The Court also offered a second explanation for its decision:
  “This underlying reason ... is reinforced by an even more vital consideration, the notion of ‘comity/ that is, a proper respect for state functions, a recognition of the fact that the entire country is made up of a Union of separate state governments, and a continuance of the belief that the National Government will fare best if the States and their institutions are left free to perform their separate functions in their separate ways. . . . The concept does not mean blind deference to ‘States’ Rights’ any more than it means centralization of control over every important issue in our National Government and its courts. The Framers rejected both these courses. What the concept does represent is a system in which there is sensitivity to the legitimate interests of both State and National Governments, and in which the National Government, anxious though it may be to vindicate and protect federal rights and federal interests, always endeavors to do so in ways that will not unduly interfere with the legitimate activities of the States.” Id., at 44.
  This concern mandates application of Younger abstention not only when the pending state proceedings are criminal, but also when certain civil proceedings are pending, if the State’s interests in the proceeding are so important that exercise of the federal judicial power would disregard the comity between the States and the National Government. E. g., Huffman v. Pursue, Ltd., 420 U. S. 592, 603-605 (1975).
  Another important reason for abstention is to avoid unwarranted determination of federal constitutional questions. When federal courts interpret state statutes in a way that raises federal constitutional questions, “a constitutional determination is predicated on a reading of the statute that is not binding on state courts and may be discredited at any time — thus essentially rendering the federal-court decision advisory and the litigation underlying it meaningless.” Moore v. Sims, 442 U. S. 415, 428 (1979). See Trainor v. Hernandez, 431 U. S. 434, 445 (1977). This concern has special significance in this case. Because Texaco chose not to present to the Texas courts the constitutional claims asserted in this case, it is impossible to be certain that the governing Texas statutes and procedural rules actually raise these claims. Moreover, the Texas Constitution contains an “open courts” provision, Art. I, § 13, that appears to address Texaco’s claims more specifically than the Due Process Clause of the Fourteenth Amendment. Thus, when this case was filed in federal court, it was entirely possible that the Texas courts would have resolved this case on state statutory or constitutional grounds, without reaching the federal constitutional questions Texaco raises in this case. As we have noted, Younger abstention in situations like this “offers the opportunity for narrowing constructions that might obviate the constitutional problem and intelligently mediate federal constitutional concerns and state interests.” Moore v. Sims, supra, at 429-430.
  Texaco’s principal argument against Younger abstention is that exercise of the District Court’s power did not implicate a “vital” or “important” state interest. Brief for Appellee 24-32. This argument reflects a misreading of our precedents. This Court repeatedly has recognized that the States have important interests in administering certain aspects of their judicial systems. E. g., Trainor v. Hernandez, supra, at 441; Middlesex County Ethics Comm. v. Garden State Bar Assn., 457 U. S. 423, 432 (1982). In Juidice v. Vail, 430 U. S. 327 (1977), we held that a federal court should have abstained from adjudicating a challenge to a State’s contempt process. The Court’s reasoning in that case informs our decision today:
  “A State’s interest in the contempt process, through which it vindicates the regular operation of its judicial system, so long as that system itself affords the opportunity to pursue federal claims within it, is surely an important interest. Perhaps it is not quite as important as is the State’s interest in the enforcement of its criminal laws, Younger, supra, or even its interest in the maintenance of a quasi-criminal proceeding such as was involved in Huffman, supra. But we think it is of sufficiently great import to require application of the principles of those cases.” Id., at 335.
  Our comments on why the contempt power was sufficiently important to justify abstention also are illuminating: “Contempt in these cases, serves, of course, to vindicate and preserve the private interests of competing litigants, . . . but its purpose is by no means spent upon purely private concerns. It stands in aid of the authority of the judicial system, so that its orders and judgments are not rendered nugatory.” Id., at 336, n. 12 (citations omitted).
  The reasoning of Juidice controls here. That case rests on the importance to the States of enforcing the orders and judgments of their courts. There is little difference between the State’s interest in forcing persons to transfer property in response to a court’s judgment and in forcing persons to respond to the court’s process on pain of contempt. Both Juidice and this case involve challenges to the processes by which the State compels compliance with the judgments of its courts. Not only would federal injunctions in such cases interfere with the execution of state judgments, but they would do so on grounds that challenge the very process by which those judgments were obtained. So long as those challenges relate to pending state proceedings, proper respect for the ability of state courts to resolve federal questions presented in state-court litigation mandates that the federal court stay its hand.
  B
  Texaco also argues that Younger abstention was inappropriate because no Texas court could have heard Texaco’s constitutional claims within the limited time available to Texaco. But the burden on this point rests on the federal plaintiff to show “that state procedural law barred presentation of [its] claims.” Moore v. Sims, 442 U. S., at 432. See Younger v. Harris, 401 U. S., at 45 (‘“The accused should first set up and rely upon his defense in the state courts, even though this involves a challenge of the validity of some statute, unless it plainly appears that this course would not afford adequate protection’”) (quoting Fenner v. Boykin, 271 U. S. 240, 244 (1926)).
  Moreover, denigrations of the procedural protections afforded by Texas law hardly come from Texaco with good grace, as it apparently made no effort under Texas law to secure the relief sought in this case. Cf. Middlesex County Ethics Comm. v. Garden State Bar Assn., supra, at 435 (rejecting on similar grounds an assertion about the inhospita-bility of state procedures to federal claims). Article VI of the United States Constitution declares that “the Judges in every State shall be bound” by the Federal Constitution, laws, and treaties. We cannot assume that state judges will interpret ambiguities in state procedural law to bar presentation of federal claims. Cf. Ohio Civil Rights Comm’n v. Dayton Christian Schools, Inc., 477 U. S. 619, 629 (1986) (assuming that a state administrative commission would “construe its own statutory mandate in the light of federal constitutional principles”). Accordingly, when a litigant has not attempted to present his federal claims in related state-court proceedings, a federal court should assume that state procedures will afford an adequate remedy, in the absence of unambiguous authority to the contrary.
  The “open courts” provision of the Texas Constitution, Article I, § 13, see nn. 10, 11, supra, has considerable relevance here. This provision has appeared in each of Texas’ six Constitutions, dating back to the Constitution of the Republic of Texas in 1836. See LeCroy v. Hanlon, 713 S. W. 2d 335, 339, and n. 4 (Tex. 1986). According to the Texas Supreme Court, the provision “guarantees all litigants . . . the right to their day in court.” Id., at 341. “The common thread of [the Texas Supreme Court’s] decisions construing the open courts provision is that the legislature has no power to make a remedy by due course of law contingent on an impossible condition.” Nelson v. Krusen, 678 S. W. 2d 918, 921 (Tex. 1984). In light of this demonstrable and longstanding commitment of the Texas Supreme Court to provide access to the state courts, we are reluctant to conclude that Texas courts would have construed state procedural rules to deny Texaco an effective opportunity to raise its constitutional claims.
  Against this background, Texaco’s submission that the Texas courts were incapable of hearing its constitutional claims is plainly insufficient. Both of the courts below found that the Texas trial court had the power to consider constitutional challenges to the enforcement provisions. The Texas Attorney General filed a brief in the proceedings below, arguing that such relief was available in the Texas courts. See Brief for Intervenor-Appellant in Nos. 86-7046, 86-7052 (CA2), pp. 32-33. Texaco has cited no statute or case clearly indicating that Texas courts lack such power. Accordingly, Texaco has failed to meet its burden on this point.
  In sum, the lower courts should have deferred on principles of comity to the pending state proceedings. They erred in accepting Texaco’s assertions as to the inadequacies of Texas procedure to provide effective relief. It is true that this case presents an unusual fact situation, never before addressed by the Texas courts, and that Texaco urgently desired prompt relief. But we cannot say that those courts, when this suit was filed, would have been any less inclined than a federal court to address and decide the federal constitutional claims. Because Texaco apparently did not give the Texas courts an opportunity to adjudicate its constitutional claims, and because Texaco cannot demonstrate that the Texas courts were not then open to adjudicate its claims, there is no basis for concluding that the Texas law and procedures were so deficient that Younger abstention is inappropriate. Accordingly, we conclude that the District Court should have abstained.
  Ill
  In this opinion, we have addressed the situation that existed on the morning of December 10, 1985, when this case was filed in the United States District Court for the Southern District of New York. We recognize that much has transpired in the Texas courts since then. Later that day, the Texas trial court entered judgment. See n. 5, supra. On February 12 of this year, the Texas Court of Appeals substantially affirmed the judgment. See ibid. We are not unmindful of the unique importance to Texaco of having its challenges to that judgment authoritatively considered and resolved. We of course express no opinion on the merits of those challenges. Similarly, we express no opinion on the claims Texaco has raised in this case against the Texas bond and lien provisions, nor on the possibility that Texaco now could raise these claims in the Texas courts, see n. 16, supra. Today we decide only that it was inappropriate for the District Court to entertain these claims. If, and when, the Texas courts render a final decision on any federal issue presented by this litigation, review may be sought in this Court in the customary manner.
  IV
  The judgment of the Court of Appeals is reversed. The case is remanded to the District Court with instructions to vacate its order and dismiss the complaint. The judgment of this Court shall issue forthwith.
  It is so ordered.
  A writ of execution is “[ajddressed to any sheriff or constable in the State of Texas [and] enables the official to levy on a debtor’s nonexempt real and personal property, within the official’s county.” 5 W. Dorsaneo, Texas Litigation Guide § 132.02[1], p. 132-7 (1986).
  If the judgment debtor files a motion for new trial, the clerk cannot issue a writ of execution until the motion for new trial is denied or overruled by operation of law. Rule 627. If a trial judge does not act on a motion for new trial, it is deemed to be overruled by operation of law 75 days after the judgment originally was signed. Rule 329b(c).
  Filing a supersedeas bond would not prevent Pennzoil from securing judgment liens against Texaco’s real property. See Tex. Prop. Code Ann. §52.002 (1984) (directing clerk to issue an abstract of the judgment “[o]n application of a person in whose favor a judgment is rendered”; no exception for superseded judgments); Thulemeyer v. Jones, 37 Tex. 560, 571 (1872). The bond’s only effect would be to prevent Pennzoil from executing the judgment and obtaining Texaco’s property.
  A judgment debtor also may suspend execution by filing “cash or other negotiable obligation of the government of the United States of America or any agency thereof, or with leave of court, ... a negotiable obligation of any bank ... in the amount fixed for the surety bond.” Rule 14c.
  Later the same day, the Texas court entered a judgment against Texaco for $11,120,976,110.83, including prejudgment interest of approximately $600 million. During the pendency of the federal action — that now concerns only the validity of the Texas judgment enforcement procedures — the state-court action on the merits has proceeded. Texaco filed a motion for new trial, that was deemed denied by operation of law under Rule 329b(c). See n. 2, supra. Subsequently, Texaco appealed the judgment to the Texas Court of Appeals, challenging the judgment on a variety of state and federal grounds. The Texas Court of Appeals rendered a decision on that appeal on February 12, 1987. That decision affirmed the trial court’s judgment in most respects, but remitted $2 billion of the punitive damages award, reducing the principal of the judgment to $8.53 billion.
  So far as we know, Texaco has never presented to the Texas courts the challenges it makes in this case against the bond and lien provisions under federal law. Three days after it filed its federal lawsuit, Texaco did ask the Texas trial court informally for a hearing concerning possible modification of the judgment under Texas law. That request eventually was denied, because it failed to comply with Texas procedural rules.
  Texaco claimed that the judgment itself conflicted with the Pull Faith and Credit Clause, the Commerce Clause, the Williams Act, and the Securities Exchange Act of 1934. Texaco also argued that application of the Texas bond and lien provisions would violate the Due Process and Equal Protection Clauses of the Fourteenth Amendment to the Federal Constitution.
  The operative portion of the injunction provided:
  “[I]t is hereby . . . ORDERED that defendant, Pennzoil Company, its employees, agents, attorneys and servants, and all persons in active concert or participation with them who receive actual notice of this Order by personal service or otherwise, are jointly and severally enjoined and restrained, pending the trial and ultimate disposition of this action, or the further order of this Court, from taking any action of any kind whatsoever to enforce or attempt to enforce the Judgment entered in an action in the District Court for the 151st Judicial District of Texas entitled Pennzoil Company v. Texaco Inc., including, without limitation, attempting to obtain or file any judgment lien or abstract of judgment related to said Judgment (pursuant to Tex. Prop. Code Ann. §§ 52.001, et seq., or otherwise), or initiating or commencing steps to execute on said Judgment . . . .” App. to Juris. Statement A52-A53.
  The order also required Texaco to post a bond of $1 billion to secure the grant of the preliminary injunction. Id., at A53.
  Although the District Court had entered only a preliminary injunction, the Court of Appeals concluded that the record was sufficiently undisputed to justify entering a permanent injunction. Thus, it did not remand the case to the District Court for further proceedings on the merits. 784 F. 2d 1133, 1156 (1986).
  In some cases, the probability that any federal adjudication would be effectively advisory is so great that this concern alone is sufficient to justify abstention, even if there are no pending state proceedings in which the question could be raised. See Railroad Comm’n of Texas v. Pullman Co., 312 U. S. 496 (1941). Because appellant has not argued in this Court that Pullman abstention is proper, we decline to address Justice Blackmun’s conclusion that Pullman abstention is the appropriate disposition of this case. We merely note that considerations similar to those that mandate Pullman abstention are relevant to a court’s decision whether to abstain under Younger. Cf. Moore v. Sims, 442 U. S. 415, 428 (1979). The various types of abstention are not rigid pigeonholes into which federal courts must try to fit cases. Rather, they reflect a complex of considerations designed to soften the tensions inherent in a system that contemplates parallel judicial processes.
  Article I, § 13, provides: “All courts shall be open, and every person for an injury done him, in his lands, goods, person or reputation, shall have remedy by due course of law.”
  See LeCroy v. Hanlon, 713 S. W. 2d 335, 340-341 (Tex. 1986) (“The open courts provision must have been intended to provide rights in addition to those in the due process provision or the former would be surplus-age. Furthermore, the due process provision’s general guarantees contrast with the open courts provision’s specific guarantee of a right of access to the courts”); id., at 338 (noting that the Texas Supreme Court “has been in the mainstream” of the movement of “state courts ... to look to their own constitutions to protect individual rights”) (citing, inter alia, Brennan, State Constitutions and the Protection of Individual Rights, 90 Harv. L. Rev. 489 (1977)). See also Dillingham v. Putnam, 109 Tex. 1, 14 S. W. 303 (1890) (invalidating a previous supersedeas bond statute because it effectively prevented certain parties from securing an appeal).
  The relevance of the open courts provision to this ease is not limited to its indication that the Texas courts may well accept Texaco’s challenge on state constitutional grounds, obviating the need for consideration of the federal constitutional questions. As we explain infra, at 15-16, this provision also undercuts Texaco’s claim that no Texas court was open to hear its constitutional claims.
  Thus, contrary to Justice Stevens’ suggestion, the State of Texas has an interest in this proceeding “that goes beyond its interest as adjudicator of wholly private disputes.” Post, at 30, n. 2. Our opinion does not hold that Younger abstention is always appropriate whenever a civil proceeding is pending in a state court. Rather, as in Juidice, we rely on the State’s interest in protecting “the authority of the judicial system, so that its orders and judgments are not rendered nugatory,” 430 U. S., at 336, n. 12 (citations omitted).
  Texaco also suggests that abstention is unwarranted because of the absence of a state judicial proceeding with respect to which the Federal District Court should have abstained. Texaco argues that “the Texas judiciary plays no role” in execution of judgments. Brief for Appellee 25. We reject this assertion. There is at least one pending judicial proceeding in the state courts; the lawsuit out of which Texaco’s constitutional claims arose is now pending before a Texas Court of Appeals in Houston, Texas. As we explain infra this page and 15-17, we are not convinced that Texaco could not have secured judicial relief in those proceedings.
  See 784 F. 2d, at 1139; App. to Juris. Statement A104 (District Court’s Supplemental Finding of Fact 94).
  Texaco relies on the language of Texas Rule of Civil Procedure 364, that lists no exceptions to the requirement that an appellant file a bond to suspend execution of a money judgment pending appeal. Texaco also relies on cases noting that Rule 364 requires appellants to post bond in the full amount of the judgment. E. g., Kennesaw Life & Accident Insurance Co. v. Streetman, 644 S. W. 2d 915, 916-917 (Tex. App. 1983) (writ refused n.r.e.). But these cases do not involve claims that the requirements of Rule 364 violate other statutes or the Federal Constitution. Thus, they have “absolutely nothing to say with respect to” Texaco’s claims that Rule 364 violates the Federal Constitution. See Huffman v. Pursue, Ltd., 420 U. S. 592, 610 (1975).
  Also, the language of Rule 364 suggests that a trial court could suspend the bond requirement if it concluded that application of the bond requirement would violate the Federal Constitution. Rule 364(a) provides: “Unless otherwise provided by law or these rules, an appellant may suspend the execution of the judgment by a good and sufficient bond” (emphasis added). Texaco has failed to demonstrate that Texas courts would not construe the phrase “otherwise provided by law” to encompass claims made under the Federal Constitution. We cannot assume that Texas courts would refuse to construe the Rule, or to apply their inherent powers, to provide a forum to adjudicate substantial federal constitutional claims.
  We recognize that the trial court no longer has jurisdiction over the case. See Tex. Rule Civ. Proc. 329b(e); n. 5, supra. Thus, relief is no longer available to Texaco from the trial court. But Texaco cannot escape Younger abstention by failing to assert its state remedies in a timely manner. See Huffman v. Pursue, Ltd., supra, at 607-609. In any event, the Texas Supreme Court and the Texas Court of Appeals arguably have the authority to suspend the supersedeas requirement to protect their appellate jurisdiction. See Pace v. McEwen, 604 S. W. 2d 231, 233 (Tex. Civ. App. 1980) (no writ) (suggesting that a Texas Court of Appeals has such authority).