In my '89 300E, I had that happen and a few minutes later the car started dying... It turned out to be the voltage regulator had blown. Simple fix, not too expensive.
I had a similar type of occurrence as bd37703 in our 1992 190E (2.3) and it turned out to be the OVP (over voltage protection)relay. Not too expensive (around $75) a bit of a pain to do (helps if you have small hands like I do) but only took about 1/2 hour one Friday evening.
Scotts Valley, CA.
1993 300 CE Cabriolet (A124) 131K miles
1997 C-280 133K miles
2000 BMW R1100RT 69K miles
1989 300 E 216K miles (sold)