San Francisco outfielder Barry Bonds was suspended for three games and Philadelphia reliever Ricky Bottalico was suspended for four because of their brawl last weekend.
The differing lengths is due in part to the players' positions.
"We tried to make the suspensions have equal impact," NL senior vice president Katy Feeney said.
While the suspensions were to start Wednesday, the players' association immediately appealed. Coleman must hold a hearing and issue a decision before any suspensions can begin.
"I'll appeal it, and that's it," Bonds said before Tuesday's game against the New York Mets.
Bond's hearing will not be held in New York, where the Giants started a three-game series. Coleman probably will hold the hearing in San Francisco or where the Giants are playing, according to Feeney.
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