I had exactly that sound on my E28. To make sure, get down on all fours at the rear corner of the car (not behind it!) where you can clearly see the diff while someone else engages the clutch while idling in reverse, just enough for the car to surge a foot or two backwards. If its the diff upper mounts as I suspect, the whole diff will surge up clearly and inch or more. The clunk is the sound of the diff slamming into whatever above it. If the diff doesn't move then it's probably one of the other items posted below. Check www.bimmerworld.com for polyurethane diff mounts.

Good luck!

I have a clunking sound in the rear part of my car (89 325I). It only does it when I hit the accelerator hard or let off of it quickly. It is not a continuous clunking but it just happens once at hard accelerating or decelerating. My car is an automatic. I just replaced the transmission mounts and that didn't help. I have a new center bearing and guibo that I am waiting to install until I know for sure where the sound is coming from. It almost sounds like the whole differential is shifting when I torque the drive shaft but everything is tight and secure there. Any advice would be much appreciated.