The arbitration hearing of running back Kelvin Bryant, who is seeking to escape the final two years of his contract with the U.S. Football League's Baltimore Stars and negotiate a deal to play for the Washington Redskins this season, is expected to conclude today in Philadelphia. But a decision is likely to take another six weeks, running into the beginning of training camps.

"We would like to get Mr. Bryant a decision as quickly as possible," arbitrator Richard Kashen said yesterday. Kashen said that, as a practice, he renders his verdicts 30 days after hearings have concluded. Kashen said he expects the Bryant verdict to be announced "sometime between Aug. 1 and Aug. 15."

Kashen already has heard two days of testimony from the Stars and from Bryant and his attorneys at the American Arbitration Association offices. Bryant alleges the Stars and the USFL made "numerous breaches of contract" by failing to maintain minimum standards required by a professional football team and league. The Redskins own Bryant's NFL rights by virtue of having chosen him in the seventh round of the 1983 draft . . .

A USFL owner, maintaining "we have sighted the enemy and they are us" warned more than two years ago that the league would fail unless limits on salaries were adhered to, according to a memo introduced at the USFL-NFL antitrust trial.

The letter, written Nov. 9, 1983, by Tad Taube, owner of the now-dormant Oakland Invaders, was one of a spate of documents introduced as the NFL opened its defense in the $1.69 billion antitrust suit filed by the USFL.

The USFL, which is scheduled to start fall play in September after three spring seasons, finished 20 days of testimony Wednesday during which it attempted to blame most of its problems on "anticompetitive actions" by the NFL, such as pressuring the three major television networks to deny it a contract for fall play.

The NFL's contention is that the USFL caused its own problems. NFL attorneys spent yesterday introducing documents through their first witness, former USFL commissioner Chet Simmons.