WASHINGTON—The Supreme Court on Monday made it harder for residents in a handful of states to sue for financial damages and cleanup measures to address environmental contamination that wasn't discovered until long after it took place.

The court, in an opinion by Justice Anthony Kennedy, ruled people living near a former CTS Corp. electronics plant in Asheville, N.C., can't proceed with lawsuits against the company because they were filed well after a 10-year state time limit.

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