An arbitrator heard arguments from attorneys Thursday in a bid by the Washington Redskins and Dallas Cowboys to challenge salary cap reductions imposed on them by the NFL in March.

There was no immediate indication after Thursday’s hearing whether the arbitrator, Stephen Burbank, had issued a ruling in the case.

The hearing in Philadelphia was closed to the public and the media. Arbitration proceedings are confidential under the sport’s collective bargaining agreement. The league and the Redskins declined to comment.

“We got a chance to present some of our issues, and the league presented some of their issues, and we’ll leave it at that,” Redskins general manager Bruce Allen said Thursday evening at the team’s 80th anniversary celebration. “We just have to let the process play out.”

Allen said the team wasn’t given a timetable on what comes next, or how long it would take for a ruling to be issued.

Several people familiar with the matter said earlier this week that the hearing was expected to focus primarily on jurisdictional issues. They did not anticipate an immediate ruling by Burbank.

The jurisdictional issues include whether the Redskins and Cowboys have the right to bring a case before Burbank because the league and the NFL Players Association agreed to the salary cap reductions.

The league has asked Burbank to dismiss the case, based on the union’s agreement to the salary cap cuts. It is not clear when Burbank will rule on that request.

The Redskins lost $36 million in cap space over two years and the Cowboys lost $10 million over the same period. The league concluced, according to people familiar with the case, that the teams violated no salary cap rules but sought to gain an unfair competitive advantage by sharply increasin player salaries for the 2010 season, which was played without a salary cap. That allowed them to have more room when the cap was restored in 2011.

The Redskins and Cowboys have denied wrongdoing.

Burbank, a University of Pennsylvania law professor, is in charge of resolving disputes that arise from the CBA. Thursday’s hearing took place at the University of Pennsylvania’s law school.

Burbank’s decision can be appealed under the terms of the CBA.