
    ST. PAUL MERCURY INSURANCE COMPANY; et al., Plaintiffs, Haynes Best Western of Alexandria; H. L. Haynes; American General Insurance Co.; Maryland Casualty Co.; HL&H Holding Co., Plaintiffs-Appellees, v. Sonya WILLIAMSON, Individually and on behalf of her minor children; Robert T. Williamson, Individually and on behalf of his minor children, Defendants-Appellants, Abner Williamson, Appellant. St. Paul Mercury Insurance Company; et al., Plaintiffs, Haynes Best Western of Alexandria Inc.; H. L. Haynes, Mr.; H. L. Haynes, Mrs.; American General Insurance Co.; Maryland Casualty Co.; HL&H Holding Co., Plaintiffs-Appellants-Cross-Appellees, v. Sonya Williamson, Etc.; et al., Defendants, Sonya Williamson, Individually and on behalf of her minor children; Robert T. Williamson, Individually and on behalf of his minor children, Defendants-Appellees-Cross-Appellants, and Abner Williamson; Dixie Williamson, Appellants.
    Nos. 01-30648, 01-30879, 02-30215 and 02-30298.
    United States Court of Appeals, Fifth Circuit.
    May 27, 2003.
    
      W. Gerald Gaudet (argued), Jeremy Ashley Hebert, Voorhies & Labbe, Lafayette, LA, Robert Emmett Kerrigan, Jr. (argued), Deutsch, Kerrigan & Stiles, New Orleans, LA, for Plaintiffs-Appellees.
    Terrance Gilroy Reed (argued), Alexandria, LA, for Defendants-Appellants.
    Before JONES, WIENER, and DeMOSS, Circuit Judges.
   WIENER, Circuit Judge:

The case before us must be the nadir in a seemingly unending series of lawsuits and counter-lawsuits in federal and state courts over the past thirteen years. In this latest iteration, Sonya and Robert Williamson (“the Williamsons”), appeal from a district court’s order preliminarily enjoining them from prosecuting one of the many actions they have filed in Louisiana state court against St. Paul Mercury Insurance Co. (“St. Paul”), Haynes Best Western of Alexandria Inc. (“Haynes Best Western”), Best Western International (“BWI”), H.L. Haynes, Mrs. H.L. Haynes, American General Insurance Co. (“American General”), and Maryland Casualty Co. (“Maryland”) (collectively, “the insurance parties”). For their part, the insurance parties have cross-appealed the district court’s denial of their request for a permanent injunction against the Williamsons in this same state action. As we determine that the district court properly refused to issue a permanent injunction against the Williamsons, which makes the district court’s preliminary injunction against the Williamsons moot, we affirm.

I.

FACTS and PROCEEDINGS

The genesis of this appeal is a 1990 lawsuit that the Williamsons filed in Louisiana state court against the insurance parties (the “original lawsuit”). In that lawsuit, the Williamsons alleged that Sonya Williamson suffered injuries resulting from an electrical shock that she purportedly incurred while all were living at the Haynes Best Western in Alexandria, Louisiana. In September 1994, a jury found that Sonya Williamson was injured, but that the injuries arose from a staged accident or fraud. The state trial court entered judgment in favor of the insurance parties, a Louisiana Court of Appeal affirmed the judgment in January 1997, and the Louisiana Supreme Court denied the Williamsons’ writ applications in June 1997.

Harken back to November 1993. While the original lawsuit was pending in the state trial court, St. Paul filed suit in federal district court against the Williamsons, claiming violations of the Racketeer Influenced and Corrupt Organizations Act (“RICO”), and alleging fraud and conspiracy under Louisiana law (the “RICO suit”). St. Paul alleged that the Williamsons had a lengthy and well-documented history of purposefully defrauding insurance companies through the filing of claims based on staged accidents and non-existent injuries. The Williamsons promptly reconvened against St. Paul; they also separately sued all of the insurance parties, making identical claims for violations of RICO and Louisiana fraud and conspiracy statutes. The RICO suit and the Williamsons’ counter-lawsuits were consolidated; and, on pretrial motions, the district court dismissed all claims, except one: It granted summary judgment to St. Paul on its claim against the Williamsons for malicious prosecution. The district court set the case for trial solely on the issue of damages. In November 1997, a jury awarded damages of $411,166.56 to St. Paul. The Wil-liamsons appealed the malicious prosecution judgment, and St. Paul appealed the dismissal of its RICO claims.

Now back to November 1995, when the RICO suit was still pending in the district court and the original lawsuit was proceeding through the state appellate courts. The Williamsons filed a petition in Louisiana state court invoking Louisiana Code of Civil Procedure (“LCCP”) article 2004 to annul the judgment in the original lawsuit that found Sonya Williamson’s injuries to be the result of either a staged accident or fraud (the “nullification suit”). Under LCCP article 2004, a “final judgment obtained by fraud or ill practices may be annulled.” Although the nullification suit remained dormant for several years, it was revived when the Williamsons filed a third supplemental and amending petition in March 1998.

This revival apparently prompted the insurance parties to file a new complaint in federal district court to enjoin the state nullification suit (the “injunction suit”). In it, the insurance parties contended that the Williamsons — via the nullification suit— were attempting to relitigate the district court’s judgment in the RICO suit (which dismissed the Williamsons’ claims against the insurance parties). In October 1998, the district court issued a preliminary injunction enjoining the Williamsons from litigating the nullification suit in state court (the “first preliminary injunction”). The Williamsons timely appealed.

As the two appeals from the RICO suit and the appeal from the injunction suit derived from the same set of facts (and prior lawsuits), we consolidated them in 1999. In August 2000, we issued our first opinion in this epic, vacating in part and affirming in part the various judgments of the district courts. Specifically, in the RICO suit, we affirmed the dismissal of the Williamsons’ claims, but vacated the judgment in favor of St. Paul on its malicious prosecution claim; we also vacated in part the district court’s dismissal of St. Paul’s RICO claims against the William-sons. In the injunction suit, we vacated the first preliminary injunction against the Williamsons, which had prevented them from prosecuting their nullification suit in state court.

Of relevance here is the portion of our August 2000 judgment that vacated the district court’s first preliminary injunction. The district court had agreed with the insurance parties that the Williamsons were attempting to relitigate the dismissal of their claims in the RICO suit, which permitted the court to issue an injunction under the relitigation exception in the Anti-Injunction Act. We held that the relitigation exception in the Anti-Injunction Act was inapplicable; noting that, under Louisiana law, a nullification action could be based on either fraud or ill practices. Although we recognized that the district court “considered and adjudged the issue of fraud” in the RICO suit, we also recognized that the record revealed that “the district court did not actually litigate an ultimate issue of fact that precludes the possibility of litigating the issue of ill practices and the corresponding nullification claim.” Thus, we concluded that on remand the district court could enjoin the Williamsons from relitigating the issue of fraud in the nullification suit as grounds for annulling the judgment under LCCP article 2004, but that it could not enjoin the Williamsons from prosecuting the nullification suit based on their claim that the insurance companies engaged in ill practices, the other nullification ground under that article.

We thus remanded the case to the district court, and the insurance parties promptly filed a motion for a permanent injunction against the Williamsons to prevent them from further prosecuting the nullification suit. Before a hearing could be held on the insurance parties’ request for a permanent injunction, however, the Williamsons returned to the state courts in search of a default judgment in the nullification suit. After some palpable forum shopping, the Williamsons eventually convinced a judge in the Civil District Court for the Parish of Orleans to issue an order, ex parte, granting them a default judgment. This effectively nullified the judgment in favor of the insurance parties in the original lawsuit.

When the insurance parties discovered what the Williamsons had done, they responded by filing (1) a motion in state court requesting a new trial and (2) motions in district court requesting sanctions and a contempt order against the William-sons. In April 2001, the district court held hearings on the insurance parties’ motions; the result was another preliminary injunction, which effectively enjoined the enforcement of the default judgment in the nullification suit (the “second preliminary injunction”). The Williamsons timely filed a notice of appeal.

While the Williamsons’ appeal was pending before us, the state court that had issued the default judgment continued proceedings apace, ignoring the second preliminary injunction. In May 2001, the state court denied the insurance parties’ motion for a new trial. The insurance parties thus returned to the district court and requested that the second preliminary injunction be amended to cover any state appellate proceedings. In June 2001, the district court agreed, expanding the scope of the second preliminary injunction accordingly.

The Williamsons petitioned us for a writ of mandamus to order the district court to vacate the second preliminary injunction. We denied the petition, reasoning that the Williamsons had timely filed their notice of appeal, which provided them with an adequate remedy.

In January 2002, before we heard the Williamsons’ appeal on the second preliminary injunction, the district court, on remand from our Williamson opinion, permanently enjoined the Williamsons from relitigating the issue of fraud in the nullification suit (the “permanent injunction”). In March 2002, the district court issued another order that (1) denied the insurance parties’ request for a permanent injunction to enjoin the Williamsons from pursuing their “ill practices” claim in the nullification suit, and (2) enjoined the Wil-liamsons, pursuant to Federal Rule of Civil Procedure 62(c), from prosecuting the nullification suit in state court while their appeal of the district court’s second preliminary injunction was pending before us. The insurance parties timely filed their notice of appeal of the order denying their request for a permanent injunction of the Williamsons’ “ill practices” claim. We again consolidated the appeals, and here we are.

II.

ANALYSIS

A. The insurance parties’ request for a permanent injunction of the William-sons’ nullity action ground in alleged “ill practices.”

1. Standard of review.

We review for abuse of discretion a district court’s denial of a motion for a permanent injunction. The application of the relitigation exception to the Anti-Injunction Act, however, is a question of law that we review de novo.

2. The district court correctly refused to enjoin the Williamsons from pursuing their “ill practices” claim.

Under the Anti-Injunction Act, a “court of the United States may not grant an injunction to stay proceedings in a State court except as expressly authorized by Act of Congress, or where necessary, in aid of its jurisdiction, or to protect of effectuate its judgments.” This statute is generally recognized to permit a district court to enjoin state court proceedings on only three bases: When it is (1) expressly authorized by a federal statute, (2) necessary to assert jurisdiction, or (3) necessary to protect or effectuate a prior judgment by a federal court.

The insurance parties urge that a permanent injunction of the William-sons’ entire nullification suit is justified under the third condition — protection or effectuation of a federal court’s judgment — commonly called the “relitigation exception.” The relitigation exception “is founded in the well-recognized concepts of res judicata and collateral estoppel.” “[A]n essential prerequisite for applying the relitigation exception is that the claims or issues which the federal injunction insulates from litigation in state proceedings actually have been decided by the federal court.”

The insurance parties contend that the district court erred in denying their request for a permanent injunction against the Williamsons’ litigating their “ill practices” claims in the nullification suit. In support of this contention, they maintain in the alternative that either (1) the relit-igation exception in the Anti-Injunction Act is applicable, or (2) the district court addressed the underlying facts of the “ill practices” claim when it adjudicated the “fraud” claim. The Williamsons respond that the insurance parties’ contentions here amount to nothing more than a thinly veiled attempt to circumvent our prior ruling in Williamson. At a minimum, urge the Williamsons, the insurance parties’ claims are precluded by the Anti-Injunction Act. In the alternative, the William-sons suggest that we should reject the insurance parties’ argument for an injunction here because the law of the case doctrine applies.

Given our earlier holding in Williamson, we find ourselves compelled to agree with the Williamsons that the law of the case doctrine applies here. We previously determined that the relitigation exception in the Anti-Injunction Act is inapplicable to the Williamsons’ “ill practices” claim in the nullification suit. “Under the law of the case doctrine, an issue of fact or law decided on appeal may not be reexamined either by the district court on remand or by the appellate court on a subsequent appeal.” Neither the law nor the underlying facts have changed since Williamson. Thus, we are shackled by the law of the case doctrine and forced to affirm the district court’s order denying the insurance parties’ request to enjoin the Williamsons from pursuing an “ill practices” claim in the nullification suit.

B. Did the district court err in preliminarily enjoining the Williamsons from prosecuting their nullification action?

The resolution of the insurance parties’ appeal concerning the permanent injunction has made the Williamsons’ appeal from the order granting the preliminary injunction moot. The preliminary injunction was superceded by the district court’s orders that (1) granted a permanent injunction prohibiting the Williamsons from pursuing a “fraud” claim in the nullification suit, and (2) denied the insurance parties’ request for a permanent injunction that would have prohibited the William-sons from pursuing an “ill practices” claim in the nullification suit. These orders effectively ended the operation of the preliminary injunction that prohibited the Wil-liamsons from prosecuting their default judgment in the nullification suit as such. Therefore, we need not address this issue.

III.

CONCLUSION

As Judge Jones noted in her dissent from the panel majority decision in Williamson: “To stage an accident for insurance tribute is reprehensible. But it’s also hard to see what good, or what collectable money judgment, may come of a RICO suit against these pathetic plaintiffs. This litigation ... should end!” We wholeheartedly agree. If it were not for our obligation to abide by the law of the case doctrine, we would gladly bury this black-flag pettifoggery, born and nurtured as it was of the parties’ amalgam of lawsuits and counter-lawsuits filed and prosecuted over the past thirteen years.

Regrettably, however, we are constrained from playing Hercules to this juridical Hydra: Lest anyone forget, we function under the stricture of federalism and the principle of comity that is exemplified in the Anti-Injunction Act. Thus, our decision to affirm the district court should not be seen in anyway as an imprimatur of what has occurred here. Simply put, the time has long since passed for this litigation to end, but the hemlock is not ours to administer: At this juncture, only the courts of Louisiana can euthanize this unseemly saga. We remain nonetheless confident that, even absent the mandate of a federal injunction, the Louisiana courts will timely drive a stake through the heart of this heretofore immortal vampire when the Williamsons further seek to prefect and enforce their ill-practices default judgment in the nullification suit.

AFFIRMED. 
      
      . St. Paul and BWI subsequently settled their claims with the Williamsons and have been dismissed from the appeal. American General and Maryland are now represented by their successor-in-interest, Zurich Insurance Company (“Zurich”), although for ease of reference, Zurich is included in the "insurance parties” designation.
     
      
      . See Williamson v. Haynes Best Western, 688 So.2d 1201 (La.Ct.App.1997).
     
      
      . 18 U.S.C. §§ 1961-68 (2000).
     
      
      . See St. Paul Mercury Ins. Co. v. Williamson, 986 F.Supp. 409 (W.D.La.1997).
     
      
      . La.Code Civ. P. art.2004 (emphasis added).
     
      
      . See St. Paul Mercury Ins. Co. v. Williamson, 224 F.3d 425 (5th Cir.2000).
     
      
      . 28 U.S.C. § 2283 (2000).
     
      
      . Williamson, 224 F.3d at 448-49.
     
      
      . Id. at 449 (emphasis added).
     
      
      . See La.Code Civ. Proc. art. 2004.
     
      
      . See In re Williamson, No. 01-30533 (5th Cir. July 25, 2001) (DeMoss, J., specially concurring) (noting that, despite being denied a default judgment by one Louisiana judge, the Williamsons "continued mightily with their search until they found a receptive ear”).
     
      
      . Id.
      
     
      
      . See In re Williamson, No. 01-30533 (5th Cir. July 25, 2001) (order denying petition for writ of mandamus).
     
      
      . Regions Bank of La. v. Rivet, 224 F.3d 483, 489 (5th Cir.2000).
     
      
      . Id.
      
     
      
      . 28 U.S.C. § 2283 (2000).
     
      
      . Atlantic Coast Line R.R. Co. v. Bhd. of Locomotive Eng’rs, 398 U.S. 281, 286, 90 S.Ct. 1739, 26 L.Ed.2d 234 (1970) (noting that the Anti-Injunction Act establishes "an absolute prohibition against enjoining state court proceedings, unless the injunction falls within one of three specifically defined exceptions").
     
      
      . Next Level Comms. L.P. v. DSC Comms. Corp., 179 F.3d 244, 249 (5th Cir.1999).
     
      
      . J.R. Clearwater, Inc. v. Ashland Chem. Co., 93 F.3d 176, 179 (5th Cir.1996) (quoting Chick Kam Choo v. Exxon Corp., 486 U.S. 140, 147, 108 S.Ct. 1684, 100 L.Ed.2d 127 (1988)).
     
      
      . Assurance Co. of Am. v. Kirkland, 312 F.3d 186, 189 (5th Cir.2002) (quoting Chick Kam Choo, 486 U.S. at 148, 108 S.Ct. 1684).
     
      
      . 224 F.3d at 448-49.
     
      
      . Id.
      
     
      
      . United States v. Matthews, 312 F.3d 652, 657 (5th Cir.2002) (quoting Tollett v. City of Kemah, 285 F.3d 357, 363 (5th Cir.2002)).
     
      
      . Obviously, all motions carried with the appeal are also denied as moot.
     
      
      . Williamson, 224 F.3d at 450 (Jones, J., dissenting).
     
      
      
        .See Chick Kam Choo, 486 U.S. at 146, 108 S.Ct. 1684 (discussing the constitutional and policy justifications for the Anti-Injunction Act).
     