A federal court hearing in Philadelphia could determine whether the NFL faces years of litigation over concussion-related brain injuries.
Thousands of former players have accused league officials of concealing what they knew about the risk of playing after a concussion.
The lawsuits allege the league glorified violence as the game became a $9 billion-a-year industry.
Some former players suffer from dementia, depression and other brain diseases, and a few have committed suicide. Others are seeking medical monitoring.
The NFL denies any fraud or negligence, and insists that player safety has always been a priority.
The league believes the complaints should go to arbitration under terms of a union contract.
U.S. District Judge Anita Brody will hear arguments Tuesday morning from Supreme Court litigators Paul Clement for the NFL and David Frederick for the players.