Volkswagen AG is nearing a $10 billion civil settlement, the largest in the auto industry’s history, to compensate U.S. owners of vehicles affected by the German car maker’s emissions-cheating scandal, said people familiar with the matter.

Under the proposed deal, Volkswagen would offer to buy back cars and provide additional compensation for owners of almost 500,000 diesel-powered vehicles with two-liter engines that contain software capable of duping government emissions tests, the people said.

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