Representatives of the NFL and its locked-out players resumed mediated talks Monday in Minneapolis as they await a pair of court rulings that could have an impact on their legal standoff.

Negotiators for the two sides reconvened with Chief Magistrate Judge Arthur J. Boylan, the mediator appointed by U.S. District Judge Susan Richard Nelson.

The two sides had four meetings with Boylan last month before the mediated talks recessed until Monday. Legal experts have said they expect little progress until other issues are resolved in court and the two sides determine how much leverage each has.

The U.S. Court of Appeals for the Eighth Circuit is still considering a request by the NFL to overturn the injunction granted by Nelson last month, which halted the lockout. Nelson ruled on April 25; four days later, the appeals court granted the league’s request for a temporary stay of that injunction. That enabled the league to re-impose the lockout.

The appellate court judges said they wanted more time to consider the NFL’s request for a longer stay of the injunction, which would keep the lockout in effect pending the league’s appeal of Nelson’s ruling.

A hearing is scheduled for June 3 in St. Louis on the NFL’s appeal. Legal experts have said the appellate court decision could come a few weeks to a couple months after the hearing.

Players have been locked out by the franchise owners since March 12. They returned to work for a single day after Nelson halted the shutdown, but were locked out again when the appellate court granted the temporary stay.

Players dissolved their union March 11 and filed an antitrust lawsuit against the owners. They contend the lockout is illegal under antitrust laws.

The two sides also are waiting for a ruling by U.S. District Judge David S. Doty on damages in a case brought by the players over the league’s television contracts.

The players are seeking $640 million in compensatory damages and three times that amount, or $1.92 billion, in punitive damages. They also are asking Doty to deny the owners access to approximately $4 billion in annual TV revenue if the lockout continues into the upcoming season. The league has asked Doty to award the players only the $6.9 million granted them in a ruling by the sport’s special master, Stephen B. Burbank.

Doty ruled in March that the league had violated an early-1990s settlement agreement that formed the basis of their longtime labor deal. The players have accused the league of improperly structuring the TV contracts to provide the owners with what would amount to a lockout fund.

Doty agreed with the players, ruling that the league failed to meet its obligation to maximize revenues that were shared with the players under the salary cap system.