They asked in U.S. District Court in New Orleans that Tagliabue recuse himself because of a conflict of interest, and also asked for a neutral arbitrator to be appointed by the court.
The NFL said it would oppose Tagliabue stepping aside.
Commissioner Roger Goodell removed himself from hearing this set of appeals and appointed his predecessor last week. But the players and their union contend Tagliabue should be disqualified because of his employment by a law firm that has handled bounty-related matters for the league and represented Goodell in Saints linebacker Jonathan Vilma's defamation lawsuit against him.
The hearings are scheduled for next Tuesday, subject to any court rulings.
The players association has concerns about "ethical and legal" issues involving Tagliabue hearing appeals by Vilma and defensive end Will Smith, Browns linebacker Scott Fujita and free- agent defensive end Anthony Hargrove.
Fujita, meanwhile, will be placed on injured reserve later this week by Cleveland and will miss the rest of the season. His suspension originally was three games, then was reduced to one by Goodell after a first set of player appeals.
Vilma was suspended for the entire season, but played last Sunday while the appeals process is in motion. Smith has a four-game suspension and Hargrove got eight games, subsequently reduced to seven. But he was cut in preseason by Green Bay and does not have a team.
The union also contends that such "pay-for programs" existed when Tagliabue was commissioner, with his knowledge.
"We have advised the union that we believe there is no basis on which former Commissioner Tagliabue should recuse himself and we will oppose any request that he do so," NFL spokesman Greg Aiello said in an email. "The appointment is consistent with the CBA and past practice, and there is no question that Commissioner Tagliabue is fully qualified to hear these appeals."
Last week, the NFL and the union discussed the possibility that Tagliabue would step in if Goodell recused himself from hearing the appeals, and the union also suggested "several outsiders" who could be used in place of Goodell.
After Tagliabue was chosen by Goodell, Vilma said:
"I think it's a good first step for Paul to be the neutral arbitrator. We expect that he is going to do things in a neutral capacity, which would be to allow us to cross-examine some of the witnesses, allow us to see more of the evidence — if there is more evidence — and be able to have a fair hearing."
Tagliabue was NFL commissioner from 1989-2006. For part of that time, Goodell was the league's general counsel.
The collective bargaining agreement with the union that was reached to end the lockout in August 2011 gave Goodell exclusive authority to hear appeals of discipline for conduct detrimental to the league or to appoint someone to hear and decide an appeal. Goodell periodically has appointed others to hear appeals for club fines, personal conduct suspensions and for matters concerning drug and steroid policy.
Goodell handed down the suspensions in May and they took effect in July after initial appeals were rejected by Goodell. Those suspensions lasted through training camp before being vacated by a three-member appeals panel that instructed Goodell to start the disciplinary process again and clarify his reasons for suspending the players.
The suspensions were reissued by the NFL two weeks ago and promptly appealed by all four players.
AP Sports Writer Brett Martel in New Orleans contributed to this report.
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