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Parallel litigation is a scenario in which different courts are hearing the same claim(s). The federal courts have a policy of not hearing (abstaining from) a case when there is parallel litigation going on in state courts, following the Colorado River abstention doctrine. In that case, the federal government sued for adjudication of certain water rights in Colorado; parties to a state court proceeding joined the U.S. as a defendant, and the Supreme Court said the federal courts should defer to that parallel litigation.
