He was replaced by Dick LeBeau, the assistant head coach and defensive coordinator who has not previously been an NFL head coach. No other staff changes were planned, Bengals officials said.
"Dick is the most knowledgeable and experienced football person on our staff, and it's appropriate he take over in this difficult situation," Bengals owner and president Mike Brown said. "He understands we are in a difficult situation, but our staff is behind him and he's eager to get at it."
Coslet resigned as the Bengals set new standards for futility, after having set an NFL record by losing 107 games in the 1990s, 108 if the Jan. 2 loss in Jacksonville, Fla., is included.
The Bengals lost 37-0 on Sunday in Baltimore. They had lost 13-0 the Sunday before in Jacksonville after a 24-7 loss at home on Sept. 10.
The Bengals have been outscored 74-7 this season. They haven't had a winning season since 1990 and have gone 10 years without making the playoffs, the longest current streak in the league.
LeBeau, 63, is a former defensive coordinator of the Pittsburgh Steelers. He oversaw the zone-blitz defenses that made the Steelers one of the NFL's top defensive teams in the mid-1990s.
LeBeau played offensive and defensive back at Ohio State, then played in the NFL for the Detroit Lions from 1959 to 1972 as a cornerback.
Coslet was promoted from offensive coordinator in October 1996 to succeed the fired Dave Shula when the Bengals were 1-6. The team finished 1996 7-2 under Coslet, giving new hope to Bengals fans deflated by years of losses under Shula.
But it was downhill from there. Under Coslet, the Bengals were 7-9 in 1997, 3-13 in 1998 and 4-12 in 1999.
Former Bengals wide receiver Carl Pickens publicly blasted the team for retaining Coslet as the 1999 season ended. The Bengals eventually released Pickens, their all-time leading receiver, who now plays for the Tennessee Titans.
The Bengals and Brown are under increased pressure to win because Hamiton County taxpayers paid for the $453 million Paul Brown Stadium in which the Bengals started play this season.
Cincinnati's total of seven points in the first three games is the lowest for a three-game stretch since the 1978 team scored three points in three weeks during a 4-12 season. Sunday's loss was the 28th in 35 games under Coslet.
"That was about as thorough a beating as you'll see," Brown said after watching the Bengals rush for just four yards in the Baltimore game.
"There have to be changes," Bengals defensive end John Copeland told the team's Web site. "Each and every player has to change what they are doing.
"It starts with the players. If we don't do it, it can't be done by anybody else," Copeland said.
The Bengals had dipped into the free-agent market during the offseason, signing safety Darryl Williams and defensive linemen Tom Barndt and Vaughn Booker.
LeBeau was defensive coordinator under former Bengals head coach Sam Wyche when Cincinnati advanced to the Super Bowl following the 1988 season. LeBeau's defense allowed an average of 11 points per game in three post-season games to get the Bengals into the Super Bowl, which they lost to the San Francisco 49ers.
LeBeau set a durability record for cornerbacks with the Detroit Lions by playing in 171 consecutive games. When he retired, his 62 career interceptions ranked third in NFL history.
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