Blatter arrived early for his scheduled 9 a.m. (0800 GMT) start with the FIFA appeal committee to challenge ethics committee sanctions imposed in December.
Platini had an eight-hour hearing on Monday. He said it focused on a verbal agreement with Blatter to get uncontracted salary for working as a presidential adviser from 1999-2002.
Platini's long-time friend, tournament organizer Jacques Lambert, was at FIFA to give evidence for a second day.
Platini said verdicts could be given Thursday or Friday.
Blatter and Platini previously said they expected their appeals to fail, then would take their cases to the Court of Arbitration for Sport.
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