Several former college football players filed class-action lawsuits Tuesday against their universities, conferences and the N.C.A.A., claiming negligence over their handling of head injuries. The spate of cases — six were filed Tuesday — marks a new effort by athletes seeking financial relief for what they say are the lasting effects from concussions sustained in their college careers. Among the named defendants in the filings are Penn State and Vanderbilt and three major football-playing conferences: the Big Ten, the Southeastern Conference and the Pacific-12.Earlier this year, a federal judge proposed a settlement in a class-action concussion lawsuit against the N.C.A.A. on behalf of all college athletes. The settlement approved by the judge included new safety protocols but no payments to any former players struggling with cognitive brain function. In contrast, when the N.F.L. was sued by a group of retired players, the league reached an agreement that included hundreds of millions of dollars for payments to help those with any of several neurological diseases.

The lawsuits filed by former college players Tuesday pertain only to football players and are separate from the original class action against the N.C.A.A. They were filed in various federal court districts around the country.

Auburn, Georgia, Oregon and Utah are the other universities targeted, though only their conferences are named defendants, along with the N.C.A.A., because of liability complications at some public institutions. The plaintiffs had careers that spanned the decades before the N.C.A.A. began requiring its members to have concussion protocols in 2010; in one case, the player competed in the 1970s. According to the filings, the players sustained concussions in college and now have a variety of health problems, including mood swings, depression and sleeplessness.

“The judge didn’t approve the original settlement because these players need financial help,” said Jay Edelson, the lead lawyer in the cases. He added that more lawsuits against more colleges and conferences were planned.

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The suits face hurdles. Hosea Harvey, a law professor at Temple, said he was skeptical of the litigation’s moving forward because proving negligence against the N.F.L. was easier than it may prove to be against colleges. He noted that the terms in the proposed N.C.A.A. settlement, which also includes $70 million for medical screenings for former college athletes, were more appropriate than seeking money from the N.C.A.A., universities or conferences.

“Absent extraordinary evidence of negligence at the time of the injury, I don’t see how the schools are culpable,” he said. “The goal should be to mitigate the harm and make things safer for players moving forward. That’s a public-health victory even if it’s not a financial one.”

The N.C.A.A. was first sued over concussions in 2011. After a number of similar cases were brought, they were consolidated. In 2014, the N.C.A.A. and the plaintiffs’ lawyers announced that they had reached a settlement. Judge John Z. Lee of United States District Court for the Northern District of Illinois approved most of the terms, but declined to give the N.C.A.A. full immunity from future class-action lawsuits. His proposal specifically allowed athletes from one university to still sue as a class. The N.C.A.A. has yet to sign off on the new terms, but now faces another round of concussion litigation.

Mr. Edelson said that each case sought its own jury trial to award damages to players and that the colleges, the conferences and the N.C.A.A. could all be liable. He declined to speculate on a potential financial payout if the former players win.

A version of this article appears in print on May 18, 2016, on page B14 of the New York edition with the headline: More Class-Action Concussion Suits Filed. Order Reprints| Today’s Paper|Subscribe