opinion: Chief Justice Rehnquist
  delivered the opinion of the Court.
  Unlike its federal counterpart, the California Arbitration Act, Cal. Civ. Proc. Code Ann. §1280 et seq. (West 1982), contains a provision allowing a court to stay arbitration pending resolution of related litigation. We hold that application of the California statute is not pre-empted by the Federal Arbitration Act (FAA or Act), 9 U. S. C. §1 et seq., in a case where the parties have agreed that their arbitration agreement will be governed by the law of California.
  Appellant Volt Information Sciences, Inc. (Volt), and ap-pellee Board of Trustees of Leland Stanford Junior University (Stanford) entered into a construction contract under which Volt was to install a system of electrical conduits on the Stanford campus. The contract contained an agreement to arbitrate all disputes between the parties “arising out of or relating to this contract or the breach thereof.” The contract also contained a choice-of-law clause providing that “[t]he Contract shall be governed by the law of the place where the Project is located.” App. 37. During the course of the project, a dispute developed regarding compensation for extra work, and Volt made a formal demand for arbitration. Stanford responded by filing an action against Volt in California Superior Court, alleging fraud and breach of contract; in the same action, Stanford also sought indemnity from two other companies involved in the construction project, with whom it did not have arbitration agreements. Volt petitioned the Superior Court to compel arbitration of the dispute. Stanford in turn moved to stay arbitration pursuant to Cal. Civ. Proc. Code Ann. § 1281.2(c) (West 1982), which permits a court to stay arbitration pending resolution of related litigation between a party to the arbitration agreement and third parties not bound by it, where “there is a possibility of conflicting rulings on a common issue of law or fact.” The Superior Court denied Volt’s motion to compel arbitration and stayed the arbitration proceedings pending the outcome of the litigation on the authority of § 1281.2(c). App. 59-60.
  The California Court of Appeal affirmed. The court acknowledged that the parties’ contract involved interstate commerce, that the FAA governs contracts in interstate commerce, and that the FAA contains no provision permitting a court to stay arbitration pending resolution of related litigation involving third parties not bound by the arbitration agreement. App. 64-65. However, the court held that by specifying that their contract would be governed by “ ‘the law of the place where the project is located,’” the parties had incorporated the California rules of arbitration, including § 1281.2(c), into their arbitration agreement. Id., at 65. Finally, the court rejected Volt’s contention that, even if the parties had agreed to arbitrate under the California rules, application of § 1281.2(c) here was nonetheless pre-empted by the FAA because the contract involved interstate commerce. Id., at 68-80.
  The court reasoned that the purpose of the FAA was “ ‘not [to] mandate the arbitration of all claims, but merely the enforcement ... of privately negotiated arbitration agreements.’” Id., at 70 (quoting Dean Witter Reynolds Inc. v. Byrd, 470 U. S. 213, 219 (1985)). While the FAA therefore pre-empts application of state laws which render arbitration agreements unenforceable, “[i]t does not follow, however, that the federal law has preclusive effect in a case where the parties have chosen in their [arbitration] agreement to abide by state rules.” App. 71. To the contrary, because “[t]he thrust of the federal law is that arbitration is strictly a matter of contract,” ibid., the parties to an arbitration agreement should be “at liberty to choose the terms under which they will arbitrate.” Id., at 72. Where, as here, the parties have chosen in their agreement to abide by the state rules of arbitration, application of the FAA to prevent enforcement of those rules would actually be “inimical to the policies underlying state and federal arbitration law,” id., at 73, because it would “force the parties to arbitrate in a manner contrary to their agreement.” Id., at 65. The California Supreme Court denied Volt’s petition for discretionary review. Id., at 87. We postponed consideration of our jurisdiction to the hearing on the merits. 485 U. S. 976 (1988). We now hold that we have appellate jurisdiction and affirm.
  Appellant devotes the bulk of its argument to convincing us that the Court of Appeal erred in interpreting the choice-of-law clause to mean that the parties had incorporated the California rules of arbitration into their arbitration agreement. See Brief for Appellant 66-96. Appellant acknowledges, as it must, that the interpretation of private contracts is ordinarily a question of state law, which this Court does not sit to review. See id., at 26, 29. But appellant nonetheless maintains that we should set aside the Court of Appeal’s interpretation of this particular contractual provision for two principal reasons.
  Appellant first suggests that the Court of Appeal’s construction of the choice-of-law clause was in effect a finding that appellant had “waived” its “federally guaranteed right to compel arbitration of the parties’ dispute,” a waiver whose validity must be judged by reference to federal rather than state law. Id., at 17, 30-36. This argument fundamentally misconceives the nature of the rights created by the FAA. The Act was designed “to overrule the judiciary’s longstanding refusal to enforce agreements to arbitrate,” Byrd, supra, at 219-220, and place such agreements “ ‘upon the same footing as other contracts,’” Scherk v. Alberto-Culver Co., 417 U. S. 506, 511 (1974) (quoting H. R. Rep. No. 96, 68th Cong., 1st Sess., 1, 2 (1924)). Section 2 of the Act therefore declares that a written agreement to arbitrate in any contract involving interstate commerce or a maritime transaction “shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract,” 9 U. S. C. § 2, and § 4 allows a party to such an arbitration agreement to “petition any United States district court... for an order directing that such arbitration proceed in the manner provided for in such agreement.”
  But §4 of the FAA does not confer a right to compel arbitration of any dispute at any time; it confers only the right to obtain an order directing that “arbitration proceed in the manner provided for in [the parties’] agreement.” 9 U. S. C. §4 (emphasis added). Here the Court of Appeal found that, by incorporating the California rules of arbitration into their agreement, the parties had agreed that arbitration would not proceed in situations which fell within the scope of Calif. Code Civ. Proc. Ann. § 1281.2(c) (West 1982). This was not a finding that appellant had “waived” an FAA-guaranteed right to compel arbitration of this dispute, but a finding that it had no such right in the first place, because the parties’ agreement did not require arbitration to proceed in this situation. Accordingly, appellant’s contention that the contract interpretation issue presented here involves the “waiver” of a federal right is without merit.
  Second, appellant argues that we should set aside the Court of Appeal’s construction of the choice-of-law clause because it violates the settled federal rule that questions of arbitrability in contracts subject to the FAA must be resolved with a healthy regard for the federal policy favoring arbitration. Brief for Appellant 49-52; id., at 92-96, citing Moses H. Cone Memorial Hospital v. Mercury Construction Carp., 460 U. S. 1, 24-25 (1983) (§2 of the FAA “create[s] a body of federal substantive law of arbitrability, applicable to any arbitration agreement within the coverage of the Act,” which requires that “questions of arbitrability ... be addressed with a healthy regard for the federal policy favoring arbitration,” and that “any doubts concerning the scope of arbitrable issues ... be resolved in favor of arbitration”); Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U. S. 614, 626 (1985) (in construing an arbitration agreement within the coverage of the FAA, “as with any other contract, the parties’ intentions control, but those intentions are generously construed as to issues of arbitrability”). These cases of course establish that, in applying general state-law principles of contract interpretation to the interpretation of an arbitration agreement within the scope of the Act, see Perry v. Thomas, 482 U. S. 483, 493, n. 9 (1987), due regard must be given to the federal policy favoring arbitration, and ambiguities as to the scope of the arbitration clause itself resolved in favor of arbitration.
  But we do not think the Court of Appeal offended the Moses H. Cone principle by interpreting the choice-of-law provision to mean that the parties intended the California rules of arbitration, including the § 1281.2(c) stay provision, to apply to their arbitration agreement. There is no federal policy favoring arbitration under a certain set of procedural rules; the federal policy is simply to ensure the enforceability, according to their terms, of private agreements to arbitrate. Interpreting a choice-of-law clause to make applicable state rules governing the conduct of arbitration — rules which are manifestly designed to encourage resort to the arbitral process — simply does not offend the rule of liberal construction set forth in Moses H. Cone, nor does it offend any other policy embodied in the FAA.
  The question remains whether, assuming the choice-of-law clause meant what the Court of Appeal found it to mean, application of Cal. Civ. Proc. Code Ann. § 1281.2(c) is nonetheless pre-empted by the FAA to the extent it is used to stay arbitration under this contract involving interstate commerce. It is undisputed that this contract falls within the coverage of the FAA, since it involves interstate commerce, and that the FAA contains no provision authorizing a stay of' arbitration in this situation. Appellee contends, however, that §§3 and 4 of the FAA, which are the specific sections claimed to conflict with the California statute at issue here, are not applicable in this state-court proceeding and thus cannot pre-empt application of the California statute. See Brief for Appellee 43-50. While the argument is not without some merit, we need not resolve it to decide this case, for we conclude that even if §§ 3 and 4 of the FAA are fully applicable in state-court proceedings, they do not prevent application of Cal. Civ. Proc. Code Ann. § 1281.2(c) to stay arbitration where, as here, the parties have agreed to arbitrate in accordance with California law.
  The FAA contains no express pre-emptive provision, nor does it reflect a congressional intent to occupy the entire field of arbitration. See Bernhardt v. Polygraphic Co., 350 U. S. 198 (1956) (upholding application of state arbitration law to arbitration provision in contract not covered by the FAA). But even when Congress has not completely displaced state regulation in an area, state law may nonetheless be preempted to the extent that it actually conflicts with federal law — that is, to the extent that it “stands as an obstacle to the accomplishment and execution of the full purposes and objectives of Congress.” Hines v. Davidowitz, 312 U. S. 52, 67 (1941). The question before us, therefore, is whether application of Cal. Civ. Proc. Code Ann. § 1281.2(c) to stay arbitration under this contract in interstate commerce, in accordance with the terms of the arbitration agreement itself, would undermine the goals and policies of the FAA. We conclude that it would not.
  The FAA was designed “to overrule the judiciary’s longstanding refusal to enforce agreements to arbitrate,” Dean Witter Reynolds Inc. v. Byrd, 470 U. S., at 219-220, and to place such agreements “ ‘upon the same footing as other contracts,’” Scherk v. Alberto-Culver Co., 417 U. S., at 511 (quoting H. R. Rep. No. 96, 68th Cong., 1st Sess., 1, 2 (1924)). While Congress was no doubt aware that the Act would encourage the expeditious resolution of disputes, its passage “was motivated, first and foremost, by a congressional desire to enforce agreements into which parties had entered.” Byrd, 470 U. S., at 220. Accordingly, we have recognized that the FAA does not require parties to arbitrate when they have not agreed to do so, see id., at 219 (the Act “does not mandate the arbitration of all claims”), nor does it prevent parties who do agree to arbitrate from excluding certain claims from the scope of their arbitration agreement, see Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U. S., at 628 (citing Prima Paint Corp. v. Flood & Conklin Mfg. Co., 388 U. S. 395, 406 (1967)). It simply requires courts to enforce privately negotiated agreements to arbitrate, like other contracts, in accordance with their terms. See Prima Paint, supra, at 404, n. 12 (the Act was designed “to make arbitration agreements as enforceable as other contracts, but not more so”).
  In recognition of Congress’ principal purpose of ensuring that private arbitration agreements are enforced according to their terms, we have held that the FAA pre-empts state laws which “require a judicial forum for the resolution of claims which the contracting parties agreed to resolve by arbitration.” Southland Corp. v. Keating, 465 U. S. 1, 10 (1984). See, e. g., id., at 10-16 (finding pre-empted a state statute which rendered agreements to arbitrate certain franchise claims unenforceable); Perry v. Thomas, 482 U. S., at 490 (finding pre-empted a state statute which rendered unenforceable private agreements to arbitrate certain wage collection claims). But it does not follow that the FAA prevents the enforcement of agreements to arbitrate under different rules than those set forth in the Act itself. Indeed, such a result would be quite inimical to the FAA’s primary-purpose of ensuring that private agreements to arbitrate are enforced according to their terms. Arbitration under the Act is a matter of consent, not coercion, and parties are generally free to structure their arbitration agreements as they see fit. Just as they may limit by contract the issues which they will arbitrate, see Mitsubishi, supra, at 628, so too may they specify by contract the rules under which that arbitration will be conducted. Where, as here, the parties have agreed to abide by state rules of arbitration, enforcing those rules according to the terms of the agreement is fully consistent with the goals of the FAA, even if the result is that arbitration is stayed where the Act would otherwise permit it to go forward. By permitting the courts to “rigorously enforce” such agreements according to their terms, see Byrd, supra, at 221, we give effect to the contractual rights and expectations of the parties, without doing violence to the policies behind by the FAA.
  The judgment of the Court of Appeals is
  Affirmed.
  Justice O’Connor took no part in the. consideration or decision of this case.
  The arbitration clause read in full as follows:
  “All claims, disputes and other matters in question between the parties to this contract, arising out of or relating to this contract or the breach thereof, shall be decided by arbitration in accordance with the Construction Industry Arbitration Rules of the American Arbitration Association then prevailing unless the parties mutually agreed [sic] otherwise. . . . This agreement to arbitrate . . . shall be specifically enforceable under the prevailing arbitration law.” App. 40.
  Volt’s motion to compel was apparently brought pursuant to §4 of the FAA, 9 U. S. C. § 4, and the parallel provision of the California Arbitration Act, Cal. Civ. Proc. Code Ann. § 1281.2 (West 1982); the motion cited both Acts as authority, but did not specify the particular sections upon which reliance was placed. App. 45-46. Volt also asked the court to stay the Superior Court litigation until the arbitration was completed, presumably pursuant to § 3 of the FAA, 9 U. S. C. § 3, and the parallel provision of the California Arbitration Act, Cal. Civ. Proc. Code Ann. § 1281.2(c)(3) (West 1982). App. 45-46.
  Section 1281.2(c) provides, in pertinent part, that when a court determines that “[a] party to the arbitration agreement is also a party to a pending court action or special proceeding with a third party, arising out of the same transaction or series of related transactions and there is a possibility of conflicting rulings on a common issue of law or fact[,] . . . the court (1) may refuse to enforce the arbitration agreement and may order intervention or joinder of all parties in a single action or special proceeding; (2) may order intervention or joinder as to all or only certain issues; (3) may order arbitration among the parties who have agreed to arbitration and stay the pending court action or special proceeding pending the outcome of the arbitration proceeding; or (4) may stay arbitration pending the outcome of the court action or special proceeding.”
  Under 28 U. S. C. §1257(2), this Court has appellate jurisdiction to review a final judgment rendered by the highest court of a State in which a decision could be had “where is drawn in question the validity of a statute of any state on the ground of its being repugnant to the Constitution, treaties or laws of the United States, and the decision is in favor of its validity.” Here appellant explicitly drew in question the validity of Cal. Civ. Proc. Code Ann. § 1281.2(c) (West 1982) on federal grounds, contending that the statute, as applied to stay arbitration of this dispute, was pre-empted by the FAA and thus invalid under the Supremacy Clause. Because the California Court of Appeal upheld application of the statute against this challenge, our appellate jurisdiction would seem to be assured. See Longshoremen v. Davis, 476 U. S. 380, 387, n. 8 (1986) (§ 1257(2) jurisdiction exists when a state statute is upheld against a claim that its application to a particular set of facts is pre-empted by federal law); McCarty v. McCarty, 453 U. S. 210, 219-220, n. 12 (1981) (same). Appellee contends, however, that § 1257(2) jurisdiction does not exist because the Court of Appeal’s decision did not directly .address the validity of the statute itself, but “simply uph[eld] the validity of the parties’ agreement,” which in turn required application of the statute. Brief for Appellee 4. Because an agreement is not a “statute,” appellee argues, the Court of Appeal’s decision is not one from which an appeal under § 1257(2) will lie. Id., at 4-5.
  We disagree. Our decisions establish that “a state statute is sustained within the meaning of § 1257(2) when a state court holds it applicable to a particular set of facts as against the contention that such application is invalid on federal grounds.” Japan Line, Ltd. v. Comity of Los Angeles, 441 U. S. 434, 441 (1979) (citing Cohen v. California, 403 U. S. 15, 17-18 (1971); Warren Trading Post Co. v. Arizona Tax Comm'n, 380 U. S. 685, 686, and n. 1 (1965); Bantam Books, Inc. v. Sullivan, 372 U. S. 58, 61, n. 3 (1963); Dahnke-Walker Milling Co. v. Bondurant, 257 U. S. 282, 288-290 (1921)), regardless of “the particular grounds or reasons on which the [state court’s] decision is put.” Id., at 289. In this case, appellant contended before the Court of Appeal that even if the contract required application of Cal. Civ. Proc. Code Ann. § 1281.2(c) (West 1982), the California statute, as applied to stay arbitration under this contract in interstate commerce, so conflicted with the FAA that it was invalid under the Supremacy Clause. The Court of Appeal upheld application of the statute against this chai-lenge, and under Dahnke-Walker and its progeny, that was sufficient to bring the case within the terms of § 1257(2), even though the court’s decision may have been premised on its interpretation of the contract.
  Unlike the dissent, see post at 486-487, we think the California arbitration rules which the parties have incorporated into their contract generally foster the federal policy favoring arbitration. As indicated, the FAA itself contains no provision designed to deal with the special practical problems that arise in multiparty contractual disputes when some or all of the contracts at issue include agreements to arbitrate. California has taken the lead in fashioning a legislative response to this problem, by giving courts authority to consolidate or stay arbitration proceedings in these situations in order to minimize the potential for contradictory judgments. See Calif. Civ. Proc. Code Ann. § 1281.2(c).
  While we have held that the FAA’s “substantive” provisions —§§ 1 and 2 — are applicable in state as well as federal court, see Southland Corp. v. Keating, 465 U. S. 1, 12 (1984), we have never held that §§3 and 4, which by their terms appear to apply only to proceedings in federal court, see 9 U. S. C. § 3 (referring to proceedings “brought in any of the courts of the United States”); § 4 (referring to “any United States district court”), are nonetheless applicable in state court. See Southland Corp v. Keating, supra, at 16, n. 10 (expressly reserving the question whether “§§ 3 and 4 of the Arbitration Act apply to proceedings in state courts”); see also id., at 29 (O’Connor, J., dissenting) (§§ 3 and 4 of the FAA apply only in federal court).
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