Knocking or Thumping sound. Help!

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