The families of debilitated former N.F.L. players say the league is obstructing their access to an estimated $1 billion settlement over concussions by reflexively rejecting valid claims and bogging down the process with unreasonable demands.

After a contentious five-year fight between the league and many former players who had accused the N.F.L. of hiding the dangers of head trauma, the two sides agreed in 2015 to a settlement that covers nearly every former player for the next 65 years.

Now the families and their lawyers describe a succession of roadblocks as they try to claim payouts, from as little as a few thousand dollars to potentially several million dollars, to help thousands of retired players left mentally infirm, in some cases severely, from years of hits and tackles on the league’s fields.

Of 1,400 claims filed so far, 140 have been approved, which legal experts say is startlingly low. The remaining 90 percent of those claims are in the process of being evaluated or have been sent back to the players and their lawyers to amend before they can be approved.

The 140 approved claims are worth $195 million, but the N.F.L. has written checks for only $100 million. The remainder is expected to be released after appeals are exhausted. The league has appealed eight awards that the administrator granted, and 12 players have appealed their awards, calling them too low. The administrator also randomly audits 10 percent of all claims.

When the league agreed to the settlement several years ago, retired players were told that they could expect speedy payouts, assuming the diagnoses for Alzheimer’s, Parkinson’s and other ailments covered in the settlement were in order.

But the N.F.L. installed so many safeguards and trapdoors into the deal, lawyers for the players said, that in the eight months since the court-approved administrator of the settlement began accepting claims, many players have been forced to spend months scrounging for paperwork they did not think they had to keep, finding new doctors to confirm established diagnoses and lodging time-consuming appeals.

The requests, the league said, are part of its efforts to deter potential fraud and do not represent foot-dragging or a lack of will to help the sick men. But as a result, the players now accuse the nation’s richest league, with $14 billion in revenue, of trying to wear them down so they accept smaller payouts, or none at all.

“Players will be shorted what they earned,” said Andrew Stewart, a retired defensive lineman with Parkinson’s disease who expected to receive nearly $3 million but, after a series of delays and requests, has been offered less than a third of that amount and is appealing. “This is not a settlement. This is about paying sick men as little as possible.”

Mr. Stewart, who was in the league from 1989 to 1993 and now lives in Canada, received a Parkinson’s diagnosis nearly a decade ago and has been receiving aid from two N.F.L. benefit plans. But to receive money from the settlement, he was required to get a diagnosis from an American doctor.

Alerted to some of the delays and accusations of unfairness leveled by lawyers for the players, Anita B. Brody, the federal judge overseeing the case, met with the N.F.L., the plaintiffs’ chief lawyer and a court-appointed administrator on Monday in Philadelphia to look at ways handle claims more efficiently and more transparently.

“Like an insurance company, they deny everything, and they go through a series of denials until people give up,” said Sheilla Dingus, who runs Advocacy for Fairness in Sports, an unaffiliated nonprofit group that monitors the league’s legal cases. “Unfortunately, the N.F.L. has the capital to keep this going a lot longer than some of these players will live.”

Orran Brown, the court-approved administrator of the settlement, said it was common for the parties to settlements to fine-tune their agreements to account for issues that arise. He said that players were now, for instance, being asked to turn in the raw scores from their neurocognitive exams even though that was not explicit in the original agreement.

He said the bulk of the claims that had been sent back to players were for missing paperwork. But another group of claims has been reviewed because many players were receiving identical diagnoses from the same physician, leading to questions of whether the players had been properly examined.

Mr. Brown said he understood that players and their lawyers might view these additional requirements with suspicion. But he said they were part of an effort to prevent fraud, not block real claims.

“It does seem people feel they are being nickeled and dimed on paperwork,” Mr. Brown said. “But there’s nothing nefarious or conspiratorial in this. The goal is to make sure everyone gets paid for legitimate claims.”

The former players who have filed claims are seeking up to $5 million each — though most will probably receive far less — for severe neurological diseases tied to years of head hits on the field. A total of 20,000 retired players registered so they could submit claims now or in the future from the settlement, which offers one-time cash awards for those with amyotrophic lateral sclerosis, Parkinson’s, Alzheimer’s, dementia and chronic traumatic encephalopathy, a degenerative brain disease linked to repeated head hits that is diagnosed posthumously.

Chris Seeger, the lead lawyer for the plaintiffs, said that the administration of such class-action settlements often had “growing pains” because of unanticipated problems. In this case, some former players have “pushed the envelope,” he said, by, among other things, obtaining diagnoses from psychologists, not neurologists; having doctors affirm diagnoses without examining patients; or submitting claims without the necessary medical records.

By bouncing claims back to players, the administrator is trying to address “some funny things that didn’t look right,” and to ensure that when claims are finally evaluated, they have a better chance of being approved, Mr. Seeger said.

Mr. Seeger disputes claims by lawyers who accuse the N.F.L. of foot-dragging and trying to reduce payments to players.

“Is this working perfectly? No,” Mr. Seeger said. But “if there aren’t sufficient records to support a diagnosis, then we have a problem,” he said. “The procedures are laid out, but there is early on typically confusion. Some of it is legitimate stuff that is getting worked out.”

Many lawyers for the players do not agree with that explanation. The high number of claims that have been questioned, they said, is evidence that fraud prevention is being used as a way to keep down payouts.

“I worked at State Farm for 10 years, so I understand all the tactics,” said Patrick Tighe, a lawyer in Florida who represents 90 players. “There are all sorts of ways to slow down the claims.”

All 35 claims Mr. Tighe has filed have been audited or sent back because of “deficiencies,” he said. Jim Acho, a lawyer in Michigan who represents former players, including Gale Sayers, said that just four of the nearly three dozen claims he had filed were approved, and that two of those were audited.

Jason Luckasevic, who represents dozens of former N.F.L. players, has filed more than 100 claims, and more than 85 percent of them have been flagged for deficiencies.

“The settlement was sold by the N.F.L. and Seeger as quick pay,” Mr. Luckasevic said. “This was something everyone feared. This is the N.F.L. disability plan version 2.0.”

The N.F.L., which insisted on much of the fraud prevention language in the settlement, denies that it has pushed the administrator to deliberately delay the payment of genuine claims, and it said that stricter requirements were not added after the deal was made final.

“There have been no changes in the terms of the settlement agreement or the criteria for claims approval since the settlement was finalized,” Brian McCarthy, a spokesman for the N.F.L., said in a statement, adding that neither the league nor Mr. Seeger had taken any steps to delay the payment of legitimate claims.

The frustration among players is particularly acute for those whose neurological diseases were diagnosed years before the settlement was approved, and who are receiving benefits for those ailments from the N.F.L. under one of its regular disability plans. The delays are making it harder for them to cover escalating medical costs and, in some cases, to repay high-interest loans they took out using their settlement as collateral.

Yet many players are afraid to speak publicly about their cases because they fear the N.F.L. will deny their claims or strip them of other benefits.

Mr. Stewart, one of the few who would talk, said the league must be held accountable. He was found to have Parkinson’s disease in 2009, when he was 43.

Mr. Stewart expected to receive a gross award of $2.8 million from the concussions settlement. But after he filed a claim, he was told that another doctor had to confirm his diagnosis.

The new diagnosis, though, would have applied to his current age, 51, which would have reduced his award by $1.2 million because in the settlement, older players are paid less than younger players on the presumption that their disease is related to age, not football.

After Mr. Stewart submitted much additional paperwork, the administrator recognized the earlier diagnosis. But the award was reduced to $750,000 because the administrator calculated he had played only one season, not four.

In the deal, the more eligible seasons a player has, the higher the exposure and the higher the award. But the number of seasons is reduced if players spent time on the injured reserved list because they presumably were not exposed to head hits then.

Mr. Stewart does not dispute being injured for parts of his career. But in his day, coaches forced him to keep practicing — often with the aid of painkillers — so he was exposed to head hits even if he did not play on game day.

In many ways, the N.F.L. case is different from many settlements, experts said. Most settlements describe the kinds of documents to support claims, like a credit card number or a receipt. In the N.F.L. settlement, many retirees are applying for benefits for dementia, which can be complicated to diagnose because it is more subjective than, say, A.L.S.

Because awards can reach millions of dollars, the players’ lawyers — many of whom receive a percentage any settlement — have an incentive to make their clients look worse than they may be, a reason for the N.F.L. to be alert to fraud, experts said.

Indeed, when the deal was first announced in 2013, the N.F.L. agreed to pay $765 million. But players feared the money would run out before every claim was filed, so the league agreed to “uncap” payments. In return for unlimited liability, the N.F.L. insisted on stronger rules to block fraudulent claims.

But the slow pace of approved claims has raised questions about whether those rules were meant to do more than fight fraud.

Kenneth Feinberg, who has administered large class-action settlements, including those related to the BP oil spill and the attacks on Sept. 11, 2001, said that in the cases he had handled, defendants had a right to try to prevent fraud. But the delays that have come from questioning a large number of claims can erode trust in the settlement.

“It’s not just how many claims have been found eligible, but how quickly the money goes out the door,” said Mr. Feinberg, who is not involved in the N.F.L. case. “All the words in the world are no substitute for visible evidence of generosity, and checks flowing to families in need.”