One of the major trade problems of the new year is one left over from the old year: How can American car makers compete with the Japanese?

In addition, government trade experts will be faced with export trading-company legislation and efforts to remove not-so-less developed countries from benefits intended for the less developed.

One major trade difficulty already has been solved. Last month Japan and the United States agreed to open more than $8 billion in Japanese government procurement to international competition, including the $3.3-billion-a-year business with Japan's Nippon Telephone and Telegraph public corporation. But some nontariff barriers imposed by the Japanese still remain, according to Malcolm Baldrige, secretary of commerce-designate. s

One of the remaining problems will be cars. Detroit had hoped that at least the trade aspect of its financial and employment problems would be solved during the last Congress when Ford Motor Co. and the United Auto Workers union pushed hard for relief.

Ford and the UAW asked Congress to pass legislation giving the president authority to negotiate an agreement limiting the numbers of cars and trucks sold in this country from Japan. The measure made a long journey from the House Ways and Means trade subcommittee to the Senate, where it was killed on the next-to-last day of the session.

The bill died after Sen. Adlai E. Stevenson (D-Ill.) threatened to filibuster the legislation if it ever reached the Senate floor. After much speechmaking and fanfare, the bill's supporters, Sens. Donald W. Riegle Jr. (D-Mich.) and Carl Levin (D-Mich.) allowed the bill to die.

Sen. John C. Danforth (R-Mo.), incoming chairman of the Senate Finance subcommittee on trade, has said that he will hold hearings on the auto industry's problems on Wednesday and Thursday and shortly afterward propose legislation to help it.

The auto industry has claimed that Japanese imports were the cause of as many as 300,000 laid-off autoworkers and billions of dollars in losses by the Big Three automakers this year.

"There's tremendous concern about damage being done to the domestic industry," Riegle said following the bill's defeat in the Senate last month. "With the prime (interest rate) at 20 percent, unless the Japanese show restraint we face the prospect of further damage aand permanent damage" to the industry, the nation's industrial base and auto-related industries.

"Unless restraint is shown . . . starting early next year, we'll be in a different parliamentary session," and the Senate could act to restrict imports, Riegle continued. "The Japanese have a knife at our throats."

The Justice Department in a Dec. 29 letter to Levin said that the president already has the authority to enter into an agreement with the Japanese to seek import restraints without violating U.S. antitrust laws. President-elect Ronald Reagan hasn't said what specific action he would take to help the auto industry. But Baldrige said he would suggest that Reagan consider talking to the Japanese about the auto problem.

"What we're seeking to do here is good for both countries," Riegle said. "If Japanese manufacturers persist, it will create other problems between the two countries, and I'm very worried about that."

Another issue expected to be debated in the next Congress is the export trading bill intended to authorize commercial banks to own export trading companies. The bill's backers contended that export landing companies would help U.S. industries in the same way Japanese companies get support from their export trading companies.

Others, like public interest advocate Ralph Nader, said that if banks own equity in export trading companies, a great burden would be imposed on the regulatory agencies to maintan bank safety and soundness, and banks would be given new monopoly powers under the guise of helping small businesses. w

In another area, efforts are being made to remove countries from special tariff treatment reserved for less-developed countries. Countries such as Mexico, Brazil, Taiwan and South Korea no longer should receive such aid because they're more developed now, according to the AFL-CIO, which asked Congress to repeal the five-year-old law allowing poor nations to ship certain goods tariff-free to the United States.