Petitioner Americana Fabrics, Inc. brought this action in the United States District Court for the Central District of California, seeking an order compelling arbitration of its contract dispute with respondent L & L Textiles, Inc. Two other courts previously had addressed this issue. The Los Angeles County Superior Court had issued an order staying arbitration, but the United States District Court for the Southern District of New York had taken a different view and had issued an order finding an enforceable agreement to arbitrate and staying the state court proceedings.

The District Court for the Central District of California, the third court to address the issue, dismissed Americana’s petition and Americana appeals. We, the first appellate court to consider this matter, hold that, under the “last in time” rule of res judicata, the order of the District Court for the Southern District of New York was binding on the Central District, and petitioner was therefore entitled, under the Federal Arbitration Act, to an order compelling arbitration. We also hold that respondent’s arguments that the district court’s order is not appealable, and that petitioner did not raise its res judicata argument in the district court, are without merit.

Reversed and remanded.

I.

FACTS

Because the timing of events is both somewhat complicated and of controlling[*1527] importance, each material event will be set forth with clarity.

On May 21, 1982, appellant Americana Fabrics, Inc. (Americana) entered into a contract with appellee L & L Textiles, Inc. (L & L). Americana claims that the contract contains a valid clause requiring arbitration in Los Angeles of any disputes arising under the contract. L & L claims that the contract is self-contradictory on the arbitration issue and that therefore there was no meeting of the minds and there is no enforceable arbitration clause.

On May 31, 1983, Americana demanded arbitration of a dispute arising under the contract.

On June 14,1983, L & L filed an action in the Los Angeles County Superior Court (California court) seeking a stay of arbitration and a declaration that no arbitration agreement was in effect.

On July 15, 1983, Americana petitioned the U.S. District Court for the Southern District of New York (SDNY) for an order under section 4 of the Federal Arbitration Act, 9 U.S.C. § 4 (1982), compelling arbitration, and for a stay of L & L’s action in the California court. The basis for federal jurisdiction was diversity of citizenship.

On July 18, 1983, the SDNY issued an order noting that there “appealed]” to be an agreement to arbitrate and staying the California court proceeding. The order stated that “[a] final order to this effect will be entered if respondent [L & L] interposes no objections within 10 days of notice and service of this order.”

On the same day, July 18, the California court granted L & L’s motion to stay arbitration, and on July 19 the court issued an order to that effect. After reconsideration sua sponte, the court reaffirmed its order on August 4.

Within ten days of the SDNY’s order, L & L filed objections to it. The objections were:

1. That Americana had failed to provide L & L with five-day notice, required by section 4 of the Federal Arbitration Act, 9 U.S.C. § 4, of its petition to compel arbitration.

2. That the SDNY could not compel arbitration in Los Angeles, because section 4 of the Act, 9 U.S.C. § 4, authorizes district courts to compel arbitration only within their own districts.

3. That there was no enforceable arbitration agreement.

4. That the SDNY had no power to stay a previously-filed action in a California court, because section 3 of the Arbitration Act, 9 U.S.C. § 3, authorizes a district court to stay only its own proceedings, not state court proceedings, pending arbitration, and because the Anti-Injunction Act, 28 U.S.C. § 2283, forbids a district court from staying a pending state court proceeding.

5. That the July 19 order of the California court staying arbitration was binding on the merits.

On August 23, 1983 the SDNY issued its final order. The order found that L & L had received adequate notice and that any defect in notice had been cured and was therefore harmless, reaffirmed that there was an enforceable agreement to arbitrate in Los Angeles, and reasserted the SDNY’s power to stay the California court action. The SDNY accepted, however, L & L’s argument that under the Arbitration Act the SDNY was without power to order arbitration in another district.

The order stated that “[wjhile the statute requires an order to compel arbitration to be issued by the Court in which arbitration is mandated, this Court has the authority, having found an agreement to arbitrate, to stay a state court proceeding until a federal court can order the parties to proceed.” The order continued the stay of the California court action and gave Americana thirty days within which to file a petition to compel arbitration in the Central District of California (Central District; district court).

L & L did not appeal the SDNY’s final order.

[*1528] Pursuant to the SDNY’s order, Americana on September 19, 1983 petitioned the Central District for an order compelling arbitration. On November 10, 1983, the Central District, Judge Richard Gadbois, denied and dismissed the petition without opinion.

Americana appeals.

II.

ISSUES ON APPEAL

On appeal, Americana argues that the order of the SDNY is res judicata and establishes that there is an enforceable agreement to arbitrate. Americana argues that the California court’s order was invalid because it was issued in violation of the stay imposed by the SDNY.

L & L argues that the order of the California court staying arbitration is res judicata and establishes that there is not an enforceable agreement to arbitrate. L & L offers the same objections to the SDNY’s order that it argued before the SDNY. L & L also argues that Americana failed to raise its res judicata argument in the court below, and that that court’s order dismissing Americana’s petition is not appealable.

We will discuss in turn the issue of appealability, the question whether Americana’s res judicata argument was raised in the court below, and the res judicata effect of the proceedings in the SDNY and the California court. Because we find that consideration of L & L’s objections to the SDNY’s order is barred by res judicata, we do not discuss the substance of those objections. Similarly, because we find that the SDNY’s order, rather than that of the California court, is binding on the Central District, we need not discuss the effect of the SDNY’s stay of the California court’s proceedings.

III.

APPEALABILITY

The Central District’s order of November 10, 1983, which denied and dismissed Americana’s petition to compel arbitration, completely and finally disposed of the only claim before that court. It is therefore appealable as a final order under 28 U.S.C. § 1291.

L & L argues, citing Langley v. Colonial Leasing Co. of New England, 707 F.2d 1 (1st Cir.1983), that because there is another action pending between L & L and Americana in the California court, the Central District’s order is not appealable. Langley, however, is completely inapposite. Langley was concerned with the appealability of the denial of a motion to compel arbitration when other issues are still pending in the same action in the same court. There is no authority for the proposition that a final order of a district court is rendered unappealable by the pendency of another action in another court. L & L’s argument is therefore totally without merit.

IV.

THE RES JUDICATA ISSUE

A. Failure to Assert Res Judicata

L & L’s second argument, that Americana failed to raise below the contention that the orders of the SDNY are res judicata, is equally devoid of merit. Americana’s petition in the Central District states that it is “based upon the orders” of the SDNY. Copies of the SDNY’s orders are attached to the petition. The petition describes and quotes from the SDNY’s final order, and characterizes it as “law of the case.” Americana's “Reply Affirmation” in response to L & L’s motion to dismiss Americana’s petition repeatedly asserts that the SDNY’s order is res judicata. The issue of the res judicata effect of the SDNY’s orders was unquestionably before the district court. We therefore proceed to the merits of that issue.

B. The Merits of the Res Judicata Issue

The doctrine of res judicata “ensures the finality of decisions.” Brown v. [*1529] Felsen, 442 U.S. 127, 131, 99 S.Ct. 2205, 2209, 60 L.Ed.2d 767 (1979). It serves to protect adversaries from the expense and vexation attending multiple lawsuits, to conserve judicial resources, and to foster reliance on judicial action by minimizing the possibility of inconsistent decisions. Montana v. United States, 440 U.S. 147, 153-54, 99 S.Ct. 970, 973-74, 59 L.Ed.2d 210 (1979). The doctrine applies to jurisdictional issues as well as substantive issues. See Durfee v. Duke, 375 U.S. 106, 84 S.Ct. 242, 11 L.Ed.2d 186 (1963); Stoll v. Gottlieb, 305 U.S. 165, 59 S.Ct. 134, 83 L.Ed. 104 (1938); Yanow v. Weyerhauser Steamship Co., 274 F.2d 274, 277 (9th Cir.1959); Title v. United States, 263 F.2d 28, 30 (9th Cir.1959).

Res judicata encompasses two subsidiary doctrines, claim preclusion and issue preclusion. ^[1] Under claim preclusion, a final judgment on the merits of a claim bars subsequent litigation of that claim. Claim preclusion “prevents litigation of all grounds for, or defenses to, recovery that were previously available to the parties, regardless of whether they were asserted or determined in the prior proceeding.” Brown v. Felsen, 442 U.S. at 131, 99 S.Ct. at 2209; see Los Angeles Branch NAACP v. Los Angeles Unified School Dist., 750 F.2d 731, 737 (9th Cir.1984). The related doctrine of issue preclusion, or collateral estoppel, bars r'elitigation, even in an action on a different claim, of all “issues of fact or law that were actually litigated and necessarily decided” in the prior proceeding. Segal v. American Tel. & Tel. Co., 606 F.2d 842, 845 (9th Cir.1979); see Montana v. United States, 440 U.S. at 153, 99 S.Ct. at 973.

The principles of res judicata apply not only to successive actions in federal courts, see Baldwin v. Iowa State Traveling Men’s Ass’n, 283 U.S. 522, 51 S.Ct. 517, 75 L.Ed. 1244 (1931), but also, by virtue of the Full Faith and Credit clause of the United States Constitution, to actions in the state courts of different states. See U.S. Const, art. IV, § 1; Durfee v. Duke, 375 U.S. 106, 109, 84 S.Ct. 242, 244, 11 L.Ed.2d 186 (1963). Further, federal courts are required by statute to give res judicata effect to the judgments of state courts. See 28 U.S.C. § 1738 (1982); Allen v. McCurry, 449 U.S. 90, 96, 101 S.Ct. 411, 415, 66 L.Ed.2d 308 (1980); Porter v. Wilson, 419 F.2d 254, 258 (9th Cir.1969). Finally, a combination of constitutional and statutory considerations requires state courts to give res judicata effect to the judgments of federal courts. See Stoll v. Gottlieb, 305 U.S. 165, 170-71, 59 S.Ct. 134, 136-37, 83 L.Ed. 104 (1938); Embry v. Palmer, 107 U.S. (17 Otto) 3, 8-10, 27 L.Ed. 346, 348-49 (1882); Degnan, Federalized Res Judicata, 85 Yale L.J. 742, 744-49 (1976).

When the same claim or issue is litigated in two courts, the second court to reach judgment should give res judicata effect to the judgment of the first, regardless of the order in which the two actions were filed. See Chicago, R.I. & P. Ry. v. Schendel, 270 U.S. 611, 615-17, 46 S.Ct. 420, 422, 70 L.Ed. 757 (1926); Unger v. Consolidated Foods Corp., 693 F.2d 703, 705 (7th Cir.1982), cert. denied, 460 U.S. 1102, 103 S.Ct. 1801, 76 L.Ed.2d 366 (1983); Westwood Chem. Co. v. Kulick, 656 F.2d 1224, 1227 (6th Cir.1981). Sometimes, however, the second court does not give preclusive effect, to the judgment of the first court. This can occur when res judicata is not asserted in the second court, or when the second court decides, rightly or wrongly, that the doctrine does not apply. Should the claim or issue then come before a third court, as it did before the Central District in this case, that court is faced[*1530] with conflicting judgments from the first two courts. The governing rule to be applied is quite clear. The third court should give res judicata effect to the last previous judgment entered. See Treinies v. Sunshine Mining Co., 308 U.S. 66, 75-78, 60 S.Ct. 44, 49-50, 84 L.Ed. 85 (1939); Porter v. Wilson, 419 F.2d 254, 259 (9th Cir.1970); 18 C. Wright, A. Miller & E. Cooper, Federal Practice & Procedure, Jurisdiction § 4404 at 26 (1981); Ginsburg, Judgments in Search of Full Faith and Credit: The Last-in-Time Rule for Conflicting Judgments, 82 Harv.L.Rev. 798 (1969).

This is the rule of “last in time.” ^[2] The formal rationale behind the rule is that the implicit or explicit decision of the second court, to the effect that the first court’s judgment is not res judicata, is itself res judicata and therefore binding on the third court. See Porter, 419 F.2d at 259. The decision is not binding because it is correct; it is binding because it is last. The rule furthers the purposes of res judicata because it “end[s] the chain of relitigation ... by stopping it where it [stands]” after entry of the second court’s judgment, and thereby discourages relitigation in a third court. Id. If an aggrieved party believes that the second court erred in not giving res judicata effect to the first court’s judgment, then the proper avenue of redress is appeal of the second court’s judgment, not collateral attack in a third court. See Treinies, 308 U.S. at 77-78, 60 S.Ct. at 50; Porter, 419 F.2d at 258-59.

In this case, the application of the “last in time” rule is clear. The res judicata effect of the SDNY’s judgment dates from its order of August 23, 1983. Not only was that order formally the “final” one, but also it was in that order that the SDNY actually decided the issues after hearing L & L’s objections. ^[3] That order was the last in time. It was entered thirty-five days after the original entry of the California court’s order (July 19) and nineteen days after the California court’s reaffirmation of its order (August 4). The SDNY heard and rejected the argument that it was bound by the prior judgment of the California court. L & L did not appeal the SDNY’s order.

It follows, therefore, that the district court should have given res judicata effect to the SDNY’s order. That order has both a claim-preclusive and issue-preclusive effect on the action in the district court. Claim preclusion applies to the order because the same claim, namely, Americana’s right to arbitration arising from L & L’s alleged breach of the contract between Americana and L & L, was asserted in both actions. Issue preclusion applies to L & L’s objections to the SDNY’s order because each and every one of those objections was considered and rejected by the SDNY.

The res judicata effect of the SDNY’s judgment, as already indicated, cannot be defeated by L & L’s allegations that the SDNY contravened statutory limits on its power. See Chicot County Drainage Dist. v. Baxter State Bank, 308 U.S. 371, 377-78, 60 S.Ct. 317, 320, 84 L.Ed. 329 (1940). Those allegations were raised before, and rejected by, the SDNY, and[*1531] therefore issue preclusion bars their relitigation in the district court. See Stoll v. Gottlieb, 305 U.S. 165, 172, 59 S.Ct. 134, 137, 83 L.Ed. 104 (1938). Further, because claim preclusion extends to matters that could have been, but were not, litigated in a prior proceeding, the claim-preclusive effect of the SDNY’s judgment would be immune from L & L’s attack even if the allegations had not been raised in the prior proceeding. See Chicot County, 308 U.S. at 378, 60 S.Ct. at 320.

For the same reasons, L & L’s argument that Americana failed to provide the statutorily-required five-day notice of its petition in the SDNY is equally unavailing. The SDNY found the alleged failure to be cured and harmless; both claim preclusion and issue preclusion prevent us from questioning that finding.

L & L argues that the failure of notice deprived the SDNY of personal jurisdiction over L & L. Lack of personal jurisdiction over a party may deprive a judgment of res judicata effect if that party did not appear in the court that rendered the judgment. See Baldwin v. Iowa State Traveling Men’s Ass’n, 283 U.S. 522, 525, 51 S.Ct. 517, 517, 75 L.Ed. 1244 (1931). L & L, however, did appear in the SDNY, where it raised its notice objection but did not explicitly raise the issue of personal jurisdiction. To the extent that the issue of personal jurisdiction was implicitly raised by the notice objection, the SDNY’s decision on that issue is binding on the district court. See Baldwin; Kendall v. Overseas Dev. Corp., 700 F.2d 536 (9th Cir.1983). To the extent that it was not, L & L waived the issue by appearing and arguing the merits of the case without raising it. See Fed.R.Civ.Pro. 12(h)(1).

V.

THE EFFECT OF THE SDNY’s ORDER

The SDNY found that there was an enforceable agreement between L & L and Americana to arbitrate in Los Angeles. Given that finding, the Central District is required to compel arbitration. Section 4 of the Federal Arbitration Act, 9 U.S.C. § 4, provides that

upon being satisfied that the making of the agreement for arbitration or the failure to comply therewith is not in issue, the court shall make an order directing the parties to proceed to arbitration in accordance with the terms of the agreement.

Given the SDNY’s finding that there is an enforceable arbitration agreement, the “making of the agreement for arbitration” is not at issue in the Central District, and there is no doubt that L & L has failed to comply with the agreement. Therefore the Central District must order arbitration.

We reverse and remand for the District Court of the Central District to order arbitration.