A multimillion-dollar award for terrorism victims will face a legal test in a New York federal appeals court this week, the latest development in a case that has pitted a group of American families against the Palestinian Authority and Palestine Liberation Organization for more than a decade.

Last year, a federal jury in Manhattan ordered the groups to pay $218.5 million to 10 families who were victims of terrorist attacks, after finding the groups liable for several shootings and bombings in Israel in the early 2000s that left 33 dead and more than 400 injured. That award was automatically tripled to $655.5 million under a U.S. antiterrorism law.

On Tuesday, the Second U.S. Circuit Court of Appeals in Manhattan is scheduled to hear arguments about whether a federal judge should have allowed the victims’ lawsuit to proceed in the U.S. in the first place.

The Palestinian Authority and PLO, the government and political representative of Palestinians in the West Bank and Gaza Strip, say the U.S. doesn’t have jurisdiction in this case.