A proceeding is parallel if it involves similar parties and similar issues. The U.S. Supreme Court has not yet addressed how federal courts should assess parallel proceedings in foreign courts (sometimes referred to as lis alibi pendens). The default approach has been to allow both cases to proceed until a judgment has been rendered in one case that may be given preclusive effect in the other. Most federal courts treat this question as one of abstention, though occasionally courts address it through forum non conveniens.

Alternatively, a U.S. court may issue an antisuit injunction ordering the parties to discontinue the suit in the other jurisdiction. There is a split among the circuits on the standard for issuing antisuit injunctions, with some courts adopting a conservative approach of granting such an injunction only if the foreign proceeding threatens the jurisdiction of the U.S. court or an important U.S. public policy and other courts adopting a liberal approach of granting such an injunction if the foreign proceeding is duplicative and vexatious.