OPINION OF THE COURT
JAMES HUNTER, III, Circuit Judge:This is an appeal from an order of the United States District Court for the Western District of Pennsylvania, which denied a motion by appellant Travelers Indemnity Company (“Travelers”) for a stay of an action brought by appellee Cost Brothers, Inc. (“Cost”) upon a payment bond issued by Travelers as surety for Frank Briscoe Company (“Briscoe”). Travelers sought the stay pending arbitration of the dispute between Cost and Briscoe. Because the district court premised its denial of the stay upon an erroneous holding that federal law governed the question of Travelers’ entitlement to the arbitration defense, we will vacate the judgment of the district court and remand for proceedings consistent with this opinion.
I
In May 1977, Briscoe entered into a contract with the Pennsylvania Department of Public Works for construction of the Pittsburgh Convention-Exposition Center. Pursuant to the Pennsylvania Public Works Contractors’ Bond Law (“PWCBL”), 8 Pa. Stat-Ann. § 193-202 (Purdon Supp.1984), Briscoe obtained performance and payment bonds on the construction contract from Travelers.
In October 1977, Briscoe engaged Cost as masonry subcontractor on the Convention-Exposition Center project. The contract between Cost and Briscoe provides for arbitration of “[a]ny controversy or claim arising out of or relating to this subcontract or the breach thereof____” Nevertheless, when Cost sought to recover allegedly overdue payments from Briscoe, it bypassed the arbitration agreement and chose instead to avail itself of the direct action against the surety, Travelers, provided by PWCBL. See 8 Pa.Stat.Ann. § 194. Cost brought an action in assumpsit in the Pennsylvania Court of Common Pleas, but Travelers obtained removal to the United States District Court for the Western District of Pennsylvania on the basis of diversity of citizenship.
Travelers moved the district court for a stay of the action pending arbitration of the dispute between Cost and Briscoe. The district court noted that in this diversity case, state law would govern the ultimate disposition of the merits. However, the district court also held that the CostBriscoe contract — an agreement between a Pennsylvania subcontractor and a New Jersey general contractor on a Pennsylvania project — involved interstate commerce within the meaning of the Federal Arbitration Act, 9 U.S.C. § 2 (1982). Based on this holding, the district court concluded that the question of Travelers’ entitlement to rely on that agreement in seeking a stay was governed by federal substantive law. The district court went on to hold as a matter of federal law that Travelers, which was not a party to the arbitration agreement, could not rely upon it. The district court therefore entered an order denying Travelers’ motion for a stay. Travelers now appeals from this order.1
*60II
The Federal Arbitration Act provides that arbitration agreements in contracts “evidencing a transaction involving [interstate] commerce ... shall be valid, irrevocable, and enforceable.” 9 U.S.C. § 2 (1982). The purpose of the Act was to abolish the common law rule that arbitration agreements were not judicially enforceable. See H.R.Rep. No. 96, 68th Cong., 1st Sess., 1 (1924); Kulukundis Shipping Co. v. Amtorg Trading Corp., 126 F.2d 978, 985 (2d Cir.1942). Thus, the Federal Arbitration Act preempts state law that might “undercut the enforceability of arbitration agreements.” Southland Corp. v. Keating, 465 U.S. 1, 104 S.Ct. 852, 861, 79 L.Ed.2d 1 (1984). Accordingly, in contracts controlled by the Act, questions of the construction of arbitration agreements and their enforceability are governed by federal substantive law. See, e.g., Southland, supra, (1984); Prima Paint Corp. v. Flood & Conklin Mfg. Co., 388 U.S. 395, 404-405, 87 S.Ct. 1801, 1806-1807,18 L.Ed.2d 1270 (1967); Becker Autoradio v. Becker Autoradiowerk GmbH, 585 F.2d 39, 43 (3d Cir.1978).
We agree with the district court that the construction of the Cost-Briscoe arbitration agreement would be a question of federal law under the Federal Arbitration Act. We also agree that Travelers, which is not a party to the agreement, may not compel Cost to submit its dispute with Travelers to arbitration. The question before the district court, however, was whether Travelers, as surety, could rely upon Cost’s failure to exhaust its arbitral remedy against Briscoe as a ground for requesting a stay, notwithstanding PWCBL’s provision of a direct action by subcontractors against sureties. This is a question of surety law that does not depend upon a construction of the arbitration agreement itself, and the resolution of this question as a matter of state surety law does not threaten to “undercut the enforceability of arbitration agreements.” Southland, 104 S.Ct. at 861. The Federal Arbitration Act, therefore, does not displace state surety law in this diversity case. See Erie v. Tompkins, 304 U.S. at 64, 78, 58 S.Ct. at 817, 822, 82 L.Ed. at 1188 (1938) (“Except in matters governed by the Federal Constitution or by Acts of commerce, the law to be applied in any case is the law of the State____ There is no federal general common law.”). The district court therefore erred in holding that Travelers’ entitlement to rely upon the arbitration agreement was governed by federal law, and we must vacate the judgment below.
Ill
The district court did not pass on the state-law question presented to it, because of its erroneous conclusion that federal law precluded Travelers from relying upon the Cost-Briscoe arbitration agreement. Moreover, the decision whether to grant a stay in this case is committed to the district court’s discretion, since it is a matter of the court’s inherent power to conserve judicial resources by controlling its own docket. See, e.g., Contracting Northwest, Inc. v. City of Fredericksburg, 713 F.2d 382, 387 *61(8th Cir.1983); American Home Assurance Co. v. Vecco Concrete Constr. Co., 629 F.2d 961, 964 (4th Cir.1980); Gavlik Constr. Co. v. H.F. Campbell Co., 526 F.2d 777, 784 (3d Cir.1975). We will therefore remand this ease for proceedings consistent with this opinion.
. Despite the interlocutory character of the district court's order, this court has jurisdiction of this appeal under the Enelow-Ettelson rule. See Ettelson v. Metropolitan Life Ins. Co., 317 U.S. 188, 63 S.Ct. 163, 87 L.Ed. 176 (1942); Enelow v. New York Life Ins. Co., 293 U.S. 379, 55 S.Ct. 310, 79 L.Ed. 440 (1935). Under this rule, an *60order by which a court grants or denies a stay of its own proceedings in an action at law pending the resolution of an equitable defense or counterclaim is analogized to an order enjoining or refusing to enjoin proceedings in another court, hearkening back to the days before the merger of law and equity. Since an order granting or denying an injunction is appealable under 28 U.S.C. § 1292(a)(1) (1982), so too is an Enelow-Ettelson order. See, e.g., Baltimore Contractors, Inc. v. Bodinger, 348 U.S. 176, 182-83, 75 S.Ct. 249, 253-54, 99 L.Ed. 233 (1955); Coastal Steel Corp. v. Tilghman Wheelabrator, Inc., 709 F.2d 190, 194 (3d Cir.), cert. denied, — U.S. -, 104 S.Ct. 349, 78 L.Ed.2d 315 (1983). Cost’s lawsuit in assumpsit is clearly an action at law. And, because an action to compel arbitration is one for specific performance on a contract, a request for a stay pending arbitration has long been regarded as an equitable claim for purposes of applying the Enelow-Ettelson rule. See Shanferoke Corp. v. Westchester Corp., 293 U.S. 449, 452-53, 55 S.Ct. 313, 314-15, 79 L.Ed. 583 (1935); Becker Autoradio v. Becker Autoradiowerk GmbH, 585 F.2d 39, 42 n. 7 (3d Cir.1978). Travelers’ appeal therefore falls squarely into the Enelow-Ettelson rule, and into this court’s jurisdiction under 28 U.S.C. § 1291(a)(1).