The suit was filed on behalf of a number of Iraqi citizens by the Center for Constitutional Rights and a number of other lawyers alleging that Blackwater had violated US and international law, as well as participating in war crimes and disobeying the Alien Tort Statute.
In November 2005, the International Labor Rights Fund, representing "tappers" (workers who extract latex from rubber trees) on the Liberian plantation, filed an Alien Tort Claims Act (ATCA) case in US District Court in California against Bridgestone (parent company owning Firestone), alleging “forced labor, the modern equivalent of slavery”, on the Firestone Plantation in Harbel, Liberia.
The U.S. Supreme Court granted certiorari (a review) on December 1, 2003, to determine the issue of whether Alvarez was entitled to remedy pursuant to the Alien Tort Statute.
He has also litigated numerous cases under the Alien Tort Claims Act and the Torture Victim Protection Act, including obtaining a $500 million judgment against Jean-Claude Duvalier, the former dictator of Haiti.
Kadic v. Karadzic, 70 F.3d 232 (2d Cir. 1996) – There was subject matter jurisdiction under the Alien Tort Claim Act, 28 U.S.C.S. § 1350, because aliens brought an action for a tort committed in violation of international law
In January, 2010, Lyman weighed in in opposition to using the U.S. Alien Tort Statute in federal court to gain reparations for South African workers, from corporations who operated in South Africa during the apartheid era.
The lawsuit, which stemmed from the firefight in Nisoor Square in Baghdad, alleged Blackwater had violated the federal Alien Tort Statute by committing extrajudicial killing and war crimes, and that the company was liable for assault and battery, wrongful death, intentional and negligent infliction of emotional distress, and negligent hiring, training and supervision.
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The Wiwa family lawsuits against Royal Dutch Shell are three separate lawsuits brought by the family of Ken Saro-Wiwa against Royal Dutch Shell, its subsidiary Shell Nigeria and the subsidiary's CEO Brian Anderson, in the United States District Court for the Southern District of New York under the Alien Tort Statute, the Torture Victim Protection Act of 1992 and Racketeer Influenced and Corrupt Organizations Act (RICO).