PHILADELPHIA » With perhaps billions of dollars at stake, a hearing Tuesday over concussion litigation filed against the NFL promises to be a contest between legal lions.

About 4,200 former players have sued the league. Some suffer from dementia, depression, Alzheimer’s disease and other neurological problems. Others simply want their health monitored.

And a small number, including Ray Easterling and 12-time Pro Bowler Junior Seau, committed suicide after long downward spirals.

The players’ lawyers accuse the NFL of promoting violence in the game and concealing known cognitive risks from concussions and other blows to the head. They hope to keep the litigation in federal court so they can use the discovery process to access NFL files — and see what the league knew when.

“The NFL failed to live up to its responsibility: it negligently heightened players’ exposure to repeated head trauma and fraudulently concealed the chronic brain injuries that resulted,” the players’ lawyers wrote in their latest brief, filed in January.

The NFL, with $9.2 billion in annual revenues, argues that the complaints belong in arbitration under terms of the collective bargaining agreement. The league insists it has always followed the best available science and made player safety a top priority.

“The rule in our league is simple: Medical decisions override everything else,” NFL Commissioner Roger Goodell said in a speech last month at the University of North Carolina.

The NFL will be represented Tuesday by Paul Clement, a former U.S. solicitor general under President George W. Bush who has fought gay marriage, gun-control measures and President Barack Obama’s state health care mandates before the Supreme Court.

Players’ lawyer David Frederick, an Obama ally, has taken consumer protection fights over investor fees and prescription drug warnings to the high court.

“They spend most of their time, Paul Clement and David Frederick, at the Supreme Court,” said Paul Anderson, a Missouri lawyer who tracks the NFL litigation on his website, nflconcussionlitigation.com. “This is really a multibillion-dollar issue. That’s why both parties went out and hired the best of the best.”

Senior U.S. District Judge Anita B. Brody of Philadelphia will hear the case and decide whether the lawsuits stay in federal court or are “pre-empted” by the collective bargaining agreements. Scores of related lawsuits around the country have been steered to her because she had been assigned the 2011 Easterling suit, the first to be filed.

If Brody sides with the players, she would then rule on some broader issues, which are expected to include hard-fought battles over the science of concussions and brain injuries, along with the players’ claims of fraud and negligence. The cases would then be returned to their home states to resolve individual damage claims, based on each player’s history.

If the NFL prevails, the players must seek individual arbitration awards. But no money is expected to change hands for years while the case plays out. Brody’s ruling, which could take months, is likely to be appealed by the losing side.

Alternatively, she could issue a mixed ruling because of a six-year “gap,” from 1987 to 1993, when there was no collective bargaining agreement in place. The NFL, eager to avoid discovery, has argued that those players were bound by previous contracts or contracts in effect when they later collected pensions.

Similarly, the league had no union contracts in place before 1968, but Anderson and others question whether those players have much of a case, since most of the scientific findings linking concussions to possible brain injuries emerged in the 1990s and later.

Goodell, in his UNC speech, called concussions “a global issue, not just a football issue.”

He said the league has pledged $30 million to the National Institutes of Health for broad-based research on the brain, which he said affects tens of millions of people. And he said the latest players’ contract sets aside another $100 million for research over the next decade.

The latest concussion study at the Boston University School of Medicine, released in January, looked at the donated brains of 85 people who had suffered head trauma in football, hockey, boxing or military combat. The study found 68 had evidence of chronic traumatic encephalopathy, the degenerative brain disease also found in Seau’s brain after the popular player shot himself in May.

“This success comes at a price to the players who make the game great,” Seau’s parents said in their lawsuit, which was consolidated with the other Brody cases last month.