DETROIT — The United Auto Workers yesterday asked a federal court in Detroit to approve a tentative agreement with General Motors Corp. that would cut benefits for 750,000 U.S. hourly workers, retirees and their families. It was another step toward what could be a sharp decline in union benefits at the Big Three U.S. automakers.

After learning of the deal between GM and the UAW, Ford Motor Co. and DaimlerChrysler AG's Chrysler Group said they'll ask the UAW for similar cuts. It's typical for automakers to match each others' agreements.

Dieter Zetsche, the former head of Chrysler who will take over as head of DaimlerChrysler next year, said he is interested in matching GM's agreement but didn't give a timeline for official talks with the UAW. Ford said it already is in talks with the union.

"The company and the UAW continue to be engaged in very private and constructive discussions to address Ford's healthcare cost reduction needs," said Joe Laymon, Ford's group vice president of human resources and labor affairs.

If UAW members ratify the agreement, GM expects to save $3 billion annually before taxes on healthcare. The agreement also would cut GM's liability for retiree healthcare by $15 billion, or 25 percent.

UAW spokesman Paul Krell said the union needs the court's approval because the settlement will cut retirees' benefits.

"It assures the retirees will be fully notified and have a right to participate in the process," Krell said.

GM shares closed down 97 cents, or 3.2 percent, at $29.12 on the New York Stock Exchange yesterday. Ford shares slid 19 cents, or 2.2 percent, to close at $8.47, and DaimlerChrysler shares fell $1.77, or 3.4 percent, to close at $49.93 on the NYSE.