The provision of the omnibus trade bills designed to promote the movement of this country's auto imports on U.S. vessels is in trouble.

In fact, a House Ways and Means sub-conference of the Senate-House conference on the bills is working on a proposal to remove the car-carriage provision, and, according to a congressional aide, It is likely to come out.Identical sections in both the House and Senate versions of the legislation would require the president to negotiate trade agreements with countries that ship 50,000 or more automobiles into the United States each year in order to provide U.S.-flag vessels with a share of that particular trade.

But the plan came under fire recently when Transportation Secretary Jim Burnley called the car-carriage provision unnecessary and unfounded.

His letter to the House Ways and Means Committee urged the sub-conference to delete it from any trade bill sent to the president.

Mr. Burnley objected to the provision because it assumes a low U.S.-flag share is the result of unfair foreign practices, and we see no reason to single out car carriage.

He pointed out the Federal Maritime Commission already has adequate authority to eliminate unfair practices, and besides that, the provision is constitutionally suspect because it interferes with the president's authority to eliminate unfair practices and negotiate treaties.

Such maritime trade agreements are, in general, contrary to U.S. trade policy and are used only in limited circumstances such as to govern trade with countries with controlled economies, said Mr. Burnley.

He added the administration has concluded that no unfair practices exist in the auto shipment market and cited an International Trade Commission conclusion in 1985 that auto shipments are open to carriers of all nations and low U.S.-flag participation is not related to discriminatory practices.

Meanwhile, The Journal of Commerce learned the trade bills' maritime sub- conference is working on a compromise proposal, concerning unfair maritime practices, that could be finished by the end of the week.

No details on the compromise were available Tuesday, but it is designed to resolve the divergent approaches toward maritime trade practices taken by the House and Senate.

The House bill would set up a trigger mechanism, based on cargo carried under hundreds of tariffs in various trade routes, that the FMC would use to determine whether transportation practices impair U.S.-flag carriers.

A less complex approach in the Senate version would clarify and expand somewhat the commission's powers under a 1920 law to investigate and address unfavorable shipping conditions.