(CNN) -- Four past or present New Orleans Saints players were suspended Wednesday by the National Football League for their roles in the "bountygate" scandal involving bonuses for trying to hurt opponents.
The league announced that Scott Fujita, Anthony Hargrove, Will Smith and Jonathan Vilma were suspended without pay for varying lengths of time.
The NFL previously suspended Saints coach Sean Payton for the 2012 season while levying an indefinite suspension on former Saints defensive coordinator Gregg Williams, who was accused of masterminding the bonus program.
Vilma, a linebacker who is still with the Saints, got suspended for a year, and teammate Smith, a defensive end, got a four-game suspension. Fujita, a linebacker with the Cleveland Browns, was suspended for three games while Hargrove, a defensive lineman now with the Green Bay Packers, got an eight-game suspension.
"It is the obligation of everyone, including the players on the field, to ensure that rules designed to promote player safety, fair play, and the integrity of the game are adhered to and effectively and consistently enforced," NFL Commissioner Roger Goodell said in a statement announcing the suspensions. "Respect for the men that play the game starts with the way players conduct themselves with each other on the field."
The statement said evidence reviewed by the league "demonstrated that from 2009-11 Saints players of their own accord pledged significant amounts of their own money toward bounties, that players accepted payments for 'cart-offs' and 'knockouts' of injured opposing players, and that the payout amounts doubled and tripled for playoff games."
Vilma was a captain of the defensive unit under Williams and assisted in creating and funding the bounty program, the NFL statement said.
"Multiple independent sources also confirmed that Vilma offered a specific bounty -- $10,000 in cash -- to any player who knocked Arizona quarterback Kurt Warner out of the 2009 Divisional Playoff Game and later pledged the same amount to anyone who knocked Minnesota quarterback Brett Favre out of the 2009 NFC Championship Game the following week," the statement said.
Hargrove "actively participated in the program" as a Saint and obstructed the league's investigation by "being untruthful," the statement said, while Fujita pledged "a significant amount of money" to the program.
Smith, a captain of the defensive unit, helped Williams with the program and pledged money for it, according to the statement.
All four players can appeal the suspensions and would be entitled to a hearing and representation by counsel, the statement said.
DeMaurice Smith, executive director of the NFL Players Association, said the organization would help the players fight the suspensions.
"After seeing the NFL's decision letters, the NFLPA has still not received any detailed or specific evidence from the league of these specific players' involvement in an alleged pay-to-injure program," Smith said in a statement. "We have made it clear that punishment without evidence is not fair. We have spoken with our players and their representatives and we will vigorously protect and pursue all options on their behalf."
In addition to the suspensions of Williams and Payton, the Saints were fined $500,000 and required to forfeit their second-round selections in the 2012 and 2013 NFL drafts.
The NFL also previously announced the suspensions of Saints General Manager Mickey Loomis for the first eight regular-season games of the 2012 season and Saints assistant head coach Joe Vitt for the first six regular-season games
The program involved as many as 27 players and at least one assistant coach, the league concluded after an investigation. Players regularly contributed cash to a pool, which may have topped $50,000 at its peak.
The players were paid $1,500 for a "knockout," when an opposing player was not able to return to the game, and $1,000 for a "cart-off," when an opposing player had to be carried off the field. In some cases, particular players on the opposing team were targeted, the NFL said.
After the program was reported on, Payton and Loomis said they took "full responsibility" for the practice, which they said "happened under our watch."