United Auto Workers members have voted to authorize a strike against Delphi Corp. if the company fails to honor its labor agreements, an action that could have severe consequences for the auto supplier and its largest customer, General Motors Corp.

More than 95 percent of UAW members who voted at 21 plants in Ohio and other states approved the strike authorization measure, the union said Tuesday. The vote doesn’t mean a strike is imminent, but it does allow the union to call a strike if it feels one is needed as the two sides bargain over wages.