National Football League executives begin their annual meeting Monday in Palm Springs, Calif., with Herschel Walker, the U.S. Football League, antitrust bills and Al Davis much on their minds.

Instead of easing, the league's headaches seem to multiply every year, despite mammoth television revenues. Twelve months ago, in Phoenix, the NFL brain trust was concerned about the expired players union contract, players' drug usage and Al Davis.

The players have a new contract and the league has made progress in the drug rehabilitation area.

The Davis problem, with its related antitrust implications, remains. And instead of worrying about player contracts, the league is concerned about the effects of the USFL, which already has depleted the draft pool significantly and has signed an undergraduate, Walker, to a lucrative long-term contract.

Although the NFL plays down the damage caused by such USFL moves, the public posturing is not convincing. The loss of even a few top-flight draft picks hurts deeply. Not having Walker to bolster interest in an injurious blow.

The executives will hear from the league's legal minds about possible future ramifications from the Walker signing, namely court challenges by other undergraduates who would play now in the pros and think about college later.

Commissioner Pete Rozelle, who seemed to spend most of 1982 in court or testifying in Congress, was back in familiar territory last week. He was a principal witness in the Los Angeles courtroom where a jury was weighing damages in the Davis-Los Angeles Coliseum Commission suit against the league for impeding the Raiders' move from Oakland.

In April, the league's appeal in that suit will be heard by a three-judge California court. In May, the City of Oakland's suit against Davis will go to trial.

In Congress, the league-backed antitrust legislation died without action last year. The NFL has not pushed yet for new legislation, although Rep. Pete Stark of Oakland introduced a bill two weeks ago that the league now is studying.

Within the league, things are not completely settled either. The DeBartolo family, which owns the San Francisco 49ers, is thinking about investing in a USFL franchise. Rozelle is expected to discuss that idea with family members at the meetings.