Tranny Problems

I have a 1999 Grand Prix GT, when I get in the car and drive off, it changes gears as smooth as a baby's rear end. After about 15 minutes, the changing starts to cluck just a little. It's not a big noise but one that you notice.
If anyone has any ideas and suggestion I would appreciate them. If there is some place to look, could you also tell me where it is physically located? Looking under the hood for wiring or sensors on this car is no easy task.
Thanks.
Jeff
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