In a decision that could complicate the Redskins’ efforts to sign free agents when the market opens Tuesday, the NFL will take $36 million in salary cap space away from the team because of its approach to structuring contracts in 2010, when there was no salary cap, according to four people familiar with the situation.

The league is taking similar action against the Dallas Cowboys, the people said. One person familiar with the matter said the Redskins would lose $36 million in cap space over two years and that Dallas would lose $10 million over the same period. The teams can decide how to distribute the cuts over the two seasons, possibly with a minimum portion that must be subtracted this year.

With about $40 million in salary cap space before the league-mandated reduction this year, the Redskins are expected to aggressively seek free agents when the market opens at 4 p.m. Tuesday. The NFL’s action could hamper them, but they will be allowed to spread the penalty over two years.

Teams also have a number of steps they can take to free up cap space, including adjusting player contracts. The Redskins released two players, Oshiomogho Atogwe and Mike Sellers, Monday.

The Redskins technically did not violate salary cap rules but attempted to gain an unfair competitive advantage in subsequent years, which were subject to a salary cap, according to the people familiar with NFL deliberations.

Redskins General Manager Bruce Allen said in a written statement released by the team: “The Washington Redskins have received no written documentation from the NFL concerning adjustments to the team salary cap in 2012 as reported in various media outlets. Every contract entered into by the club during the applicable periods complied with the 2010 and 2011 collective bargaining agreements and, in fact, were approved by the NFL commissioner’s office. We look forward to free agency, the draft and the coming football season.”

Redskins officials declined further comment.

But a person familiar with the case said while “there was no cap violation,” contracts by the team “were structured in a manner designed to secure an unfair competitive advantage” when the salary cap returned. That person said there was no basis for the league to disapprove the contracts at the time, during the uncapped year, but the league felt there was a basis to act now.

This season’s salary cap will be $120.6 million per team, a figure that includes a redistribution to other teams — except the Oakland Raiders and New Orleans Saints — of the deductions from the Redskins and Cowboys.

“All the clubs were warned not to do anything to create a competitive advantage when the salary cap came back, and that’s what [the Redskins] did,” said one of the people familiar with the matter. “They were very obvious about it. A lot of people were very angry about it. The ramifications could have been far worse for them. They could have lost draft picks. Some people recommended that to the commissioner.”

According to that person, the Redskins reworked some player contracts to pay them large sums during the uncapped 2010 season and save money against the cap in subsequent years. The person said the Redskins, in large part because of those maneuvers, had a player payroll far in excess of other teams’ payrolls.

Officials of the league and the NFL Players Association agreed to the reduction in the salary cap for the two teams in deliberations over the past week, said one person, who spoke on the condition of anonymity because of the sensitivity of the topic.

The union agreed to the resolution reluctantly, the person said. Union officials believe that neither team did anything wrong or attempted to circumvent the salary cap. But the union acquiesced to the decision because the league would have lowered the salary cap for all 32 teams if it did not.

The NFL issued a written statement that said: “The Management Council Executive Committee determined that the contract practices of a small number of clubs during the 2010 league year created an unacceptable risk to future competitive balance, particularly in light of the relatively modest salary cap growth projected for the new agreement’s early years. To remedy these effects and preserve competitive balance throughout the league, the parties to the [collective bargaining agreement] agreed to adjustments to team salary for the 2012 and 2013 seasons. These agreed-upon adjustments were structured in a manner that will not affect the salary cap or player spending on a league-wide basis.”

The year without a salary cap was a provision written into the sport’s previous labor agreement in an attempt to encourage team owners and the players’ union to extend the agreement before the uncapped year was reached. The salary cap was restored when the new labor agreement went into effect last season.