Petitioner has filed a motion "for clarification of mandate" in this case, and respondents have filed a memorandum in answer to petitioner's motion.* We decided this case last Term on June 29, 1977, 433 U.S. 623, 97 S.Ct. 2881, 53 L.Ed.2d 1009; Mr. Justice REHNQUIST delivered a plurality opinion for himself, Mr. Justice STEWART, and Mr. Justice POWELL; and Mr. Justice BLACKMUN delivered an opinion concurring in the result for himself and The Chief Justice. While these opinions did not agree in their reasoning, each of them concluded that the judgment of the Court of Appeals for the Seventh Circuit, 545 F.2d 1050, which had in turn affirmed the issuance of an injunction by the District Court for the Northern District of Illinois, 403 F.Supp. 527, should be reversed. Mr. Justice STEVENS, delivered a dissenting opinion for himself, Mr. Justice BRENNAN, Mr. Justice WHITE, and Mr. Justice MARSHALL. The dissenting Members of the Court would have affirmed the Court of Appeals for the Seventh Circuit. The judgment of the Court, using language customary in such documents, ordered "that this cause be, and the same is hereby, remanded to the United States Court of Appeals for the Seventh Circuit for further proceedings in conformity with the opinion of this Court." On August 19, 1977, the Court of Appeals in turn entered an order remanding the case to the District Court "for further proceedings, in conformity with the opinion of the United States Supreme Court rendered on June 29, 1977."

A timely petition for rehearing was filed in this Court, contending, inter alia :

"The Concurring Opinion . . . was explicitly based on the false assumption that 'only one state-court proceeding was involved in this case.' The Concurring Opinion states that 'the District Court failed properly to apply the California Motor Transport rule' because

" 'The court believed that it was enough that Vendo's activities in the single state-court proceeding involved in this case were not genuine attempts to use the state adjudicative process legitimately' [433 U.S., at 645, 97 S.Ct., at 2894].

"That interpretation of the District Court's findings is erroneous."

This petition for rehearing was denied on October 3, 1977. 434 U.S. 881, 98 S.Ct. 242, 54 L.Ed.2d 164.

Meanwhile, respondents took the position in the District Court that the injunction which it had issued continued to be binding in spite of this Court's decision, and petitioner therefore filed a motion in the District Court asking that the preliminary injunction previously issued be formally dissolved. The District Court has thus far declined to dissolve the injunction, and petitioner asserts that it has expressed the view that the preliminary injunction is still in effect until dissolved by that court, and any action by petitioner to collect its state-court judgments would risk contempt.

Respondents' memorandum in answer to petitioner's motion for clarification of judgment states, correctly we believe, that "[i]n effect, Vendo's Motion for Clarification is a petition for this Court to mandamus the District Court to grant Vendo's Motion to Dissolve." Respondents contend that the District Court was not required by the opinions and judgment of this Court to dissolve the preliminary injunction which it had earlier issued, but that the District Court should be permitted to decide Vendo's motion to dissolve before Vendo can appeal.

Respondents' memorandum in this Court sets forth their contentions made to the District Cou t after remand as to why the injunction should not be dissolved. These contentions are: (1) further findings of fact which are warranted by the record should be made in support of the injunction; (2) a finding of grave abuse of the state courts by Vendo, in seeking to further the precise conduct prescribed by the antitrust laws, is fully warranted by the record and should be made in support of the injunction; (3) the District Court should permit the record to be supplemented by further evidence newly discovered since the prior hearing; (4) the District Court should grant respondents the protection offered by Vendo's so-called consent decrees and by the representations to this Court made by Vendo in opposing a stay.

We believe that the parties are correct in treating this as an action for mandamus, which is available to a party who has prevailed in this Court if the lower court "does not proceed to execute the mandate, or disobeys and mistakes its meaning . . . ." United States v. Fossatt, 21 How. 445, 446, 16 L.Ed. 185 (1859). Put another way, "[w]hen a case has been once decided by this court on appeal, and remanded to the Circuit Court, whatever was before this court, and disposed of by its decree, is considered as finally settled. The Circuit Court is bound by the decree as the law of the case; and must carry it into execution, according to the mandate. . . . If the Circuit Court mistakes or misconstrues the decree of this court, and does not give full effect to the mandate, its action may be controlled, either upon a new appeal (if involving a sufficient amount) or by a writ of mandamus to execute the mandate of this court." In re Sanford Fork & Tool Co., 160 U.S. 247, 255, 16 S.Ct. 291, 293, 40 L.Ed. 414 (1895).

While the parties both treat petitioner's motion for clarification as a motion for leave to file a petition for a writ of mandamus, and are, we believe, correct in so doing, this Court's Rule 31 requires that the motion and petition "shall be served on the judge or judges to whom the writ is sought to be directed . . . ." There is no indication in the papers filed by either petitioner or respondents that any such service has been made. The granting of petitioner's motion for clarification of judgment would serve no useful purpose, since the judgment is typically a routine order directing that the decision of this Court be carried into effect. If petitioner is of the view that the District Court to which the case was remanded is failing to carry out the judgment of this Court, its remedy is by motion for leave to file a writ of mandamus pursuant to Rule 31, including service of the motion or petition upon the judge or judges to whom the writ would be directed. The petition for clarification of judgment is therefore denied, without prejudice to the filing of a motion for leave to file a petition for mandamus.

It is so ordered.