Per Curiam.

Petitioner has filed a motion for leave to file a petition for a writ of mandamus and requests that a writ of mandamus issue to the District Court for the First Judicial District, Santa Fe County, N. M., directing the court to vacate two orders on the ground that they violated this Court’s mandate in General Atomic Co. v. Felter, 434 U. S. 12 (1977).

In that opinion, we held that under the Supremacy Clause of the United States Constitution the Santa Fe court lacked power to enjoin the General Atomic Co. (GAC) from filing and prosecuting in personam actions against the United Nuclear Corp. (UNC) in federal court. Upon remand, the Santa Fe court modified its injunction “to exclude from its terms and conditions all in personam actions in Federal Courts and all other matters mandated to be excluded from the operation of said preliminary injunction by the opinion of *494 the United States Supreme Court, dated October 31, 1977.” Shortly thereafter, GAC filed a demand for arbitration with UNC of issues growing out of the 1973 uranium supply agreement around which the litigation between the parties revolves. This demand, filed with the American Arbitration Association, relied upon the Federal Arbitration Act, 9 U. S. C. § 1 et seq. (1976 ed.), and the arbitration clause of the 1973 agreement. GAC also filed demands for arbitration against UNC in the federal arbitration proceedings involving Duke Power Co. (Duke) and moved for permission to file a cross-claim against UNC in the arbitration proceedings involving Commonwealth Edison Co. (Commonwealth). Finally, GAC requested the Santa Fe court to stay its own trial proceedings with respect to issues subject to these arbitration demands. UNC, in addition to opposing this motion, also asked the court to stay the arbitration proceedings.

On December 16, 1977, the Santa Fe court issued a decision in which it concluded that GAC had waived any right to arbitration with UNC which it might have had because it failed to demand arbitration in a timely manner and that neither the Duke nor Commonwealth agreements gave GAC any right to demand arbitration with UNC. On the basis of these conclusions, Judge Felter filed the following order staying the arbitration proceedings:

“IT IS THEREFORE ORDERED, ADJUDGED AND DECREED that United Nuclear Corporation’s Application for Order Staying Arbitrations and Partial Final Judgment, be and the same hereby is granted.

“IT IS FURTHER ORDERED, ADJUDGED AND DECREED that further arbitration proceedings predicated upon the following demands for arbitration made by Defendant General Atomic Company against Plaintiff United Nuclear Corporation in the following arbitration proceedings, viz:

“A. The Demand for Arbitration filed by General Atomic *495 Company on November 29, 1977 with the American Arbitration Association for arbitration of the disputes arising under the 1973 Supply Agreement, a copy of which is attached to GAC’s Motion to Stay Proceedings, “B. Duke Power Company v. GAC, Case No. 31-10-0009-76, in Charlotte, North Carolina,

“C. Commonwealth Edison Company v. UNC, GAC and Gulf, Case No. 51-10-0106-74-C in Chicago, Illinois “shall be, and each of them hereby are, stayed until the further order of the Court, Provided, however, that this Partial Final Judgment shall not, in and of itself, operate to preclude Defendant General Atomic Company from asserting claimed federal rights in appropriate judicial proceedings.

“IT IS FURTHER ORDERED, DECLARED, DETERMINED AND ADJUDICATED that Defendant General Atomic Company has no right to arbitrate any issue in the aforesaid arbitration proceedings or pending herein against Plaintiff United Nuclear Corporation.”

On December 27, 1977, the court formally denied GAC’s motion to stay the trial pending completion of the arbitration proceedings.

During the course of our opinion in General Atomic Co., we specifically addressed the restrictions placed by the Santa Fe court’s previous injunction upon GAC’s attempt to assert what it believed to be federally guaranteed arbitration rights in other forums:

“What the New Mexico Supreme Court has described as ‘harassment’ is principally GAC’s desire to defend itself by impleading UNC in the federal lawsuits and federal arbitration proceedings brought against it by the utilities.11 This, of course, is something which GAC has every right to attempt to do under Fed. Rule Civ. Proc. 14 and the Federal Arbitration Act. . . . The right to pursue federal *496 remedies and take advantage of federal procedures and defenses in federal actions may no more be restricted by a state court here than in Donovan [v. Dallas, 377 U. S. 408 (1964)]. Federal courts are fully capable of preventing their misuse for purposes of harassment.” 434 U. S., at 18-19.

Footnote 11 specifically addressed arbitration proceedings which are the subject of Judge Felter’s new stay order:

“The injunction has also prevented GAC from asserting claims against UNC under the arbitration provision of the 1973 uranium supply agreement in the pending arbitration proceeding instituted against GAC and UNC by Commonwealth prior to its issuance, even though the District Court granted Commonwealth’s demand for arbitration and the Seventh Circuit has affirmed. Commonwealth Edison Co. v. Gulf Oil Corp., 400 F. Supp. 888 (ND Ill. 1975), aff’d, 541 F. 2d 1263 (1976). In addition, the Western District of North Carolina federal court has refused to stay arbitration between Duke and GAC in a proceeding also instituted prior to the injunction, despite GAC’s contention that UNC was an indispensable party to any such arbitration proceeding which it was prevented from impleading by the injunction. The court acknowledged, however, that UNC would be a proper party to the proceeding. General Atomic Co. v. Duke Power Co., 420 F. Supp. 215 (1976).”

In its order of December 16, 1977, the Santa Fe court has again done precisely what we held that it lacked the power to do: interfere with attempts by GAC to assert in federal forums what it views as its entitlement to arbitration. 1 Clearly, our *497 prior opinion did not preclude the court from making findings concerning whether GAC had waived any right to arbitrate or whether such a right was contained in the relevant agreements. Nor did our prior decision prevent the Santa Fe court, on the basis of such findings, from declining to stay its own trial proceedings as requested by GAC pending arbitration in other forums. But, as demonstrated supra, we have held that the Santa Fe court is without power under the United States Constitution to interfere with efforts by GAC to obtain arbitration in federal forums on the ground that GAC is not entitled to arbitration or for any other reason whatsoever. GAC, as we previously held, has an absolute right to present its claims to federal forums.

As was recently reaffirmed in Vendo Co. v. Lektro-Vend Corp., 434 U. S. 425 (1978), if a lower court “mistakes or misconstrues the decree of this Court, and does not give full effect to the mandate, its action may be controlled ... by a writ of mandamus to execute the mandate of this Court.” In re Sanford Fork & Tool Co., 160 U. S. 247, 255 (1895). A litigant who, like GAC, has obtained judgment in this Court after a lengthy process of litigation, involving several layers of courts, should not be required to go through that entire process again to obtain execution of the judgment of this Court. In light of the prior proceedings in this matter, it is inconceivable that upon remand from this Court the Santa Fe court was free to again impede GAC’s attempt to assert its arbitration claims in federal forums. Because the Santa Fe court has refused or failed to comply with the judgment of this Court, petitioner’s motion for leave to file a petition for a writ of mandamus is granted. Assuming as we do that the Santa Fe court will now conform to our previous judgment by promptly vacating or modifying its order of December 16, 1977, to the extent that it places any restriction whatsoever upon GAC’s exercise *498 of its right to litigate arbitration claims in federal forums, we do not at present issue a formal writ of mandamus. 2 See Bucolo v. Adkins, 424 U. S. 641 (1976); Deen v. Hickman, 358 U. S. 57 (1958).

It is so ordered.

Although the court stated that its order staying the arbitration proceedings “shall not in and of itself operate to preclude Defendant General Atomic Company from asserting its claimed federal rights in appropriate judicial proceedings,” the only plausible reading of this provision in light *497 of the stay order is that the court did not view the proceedings in question as “appropriate.”

We do not read the December 27, 1977, order as restricting GAC from pursuing its arbitration claims in other forums. Consequently there is no occasion to disturb it.