Okay, the babe's '91 300D (which used to be mine) suddenly has a new sound in it's vocabulary. It appears during acceleration from a standstill and again accelerating around corners. It does not speak in reverse or when accelerated with the brakes down firmly. What might this new thing be? As best I can tell, it's coming from the rear end, so it seems to me that it's something in the drive train (duh). Anybody have any similar experiences? Got a clue? The thumps come in rapid succession on acceleration, then once it's at speed, stops until I kick it making a turn. If your reply involves a big expense to fix this, I DO NOT what to hear it. Thanks in advance.

Kevin
'73 BMW 2002 Targa
'91 MB 300D
'95 BMW 530i

Kevin,
You need a new center bearing support mount on the drive shaft.
Not to hard to do, not an expensive part [ $20 or so ]
and considered a DIY repair if your handy.

Thump, Thump Thump
 

Arthur: The babe and I thank you for solving our mystery. Kevin

This also might be one of the rubber "donut" couplings in the drivetrain. If these let go you will get that thumping sound as the driveshaft will not remained centered. Check them all..

Don't rule out a bad CV joint on one of the axle shafts. Still not super spendy, maybe a couple hundred bucks.

According to Benzmac...
The diff mounts are known to make this kind of noise.