Have '99 Jeep Grand Cherokee - problem with automatic power door locks: Once put in gear, accelerator depressed and car moving, the doors all lock (normal)...but then continue to try and relock anytime the accelerator is depressed...???

for all doors or just a particular door?

All door locks trying to relock whenever traveling and accellerator depressed. Also have noted that when a door is opened after car has been moving that there is a clicking noise from what sounds like a relay in the drivers door...

The doors are programmed to lock when the vehicle reaches 10 or 15 mph, has nothing to do with the accelerator position. It's possible a speed sensor is bad and sending faulty speed information to the BCM.
Check for fault codes, even if the check engine light is not on there could still be fault codes set.