Very possibly indicative of low fuel pressure. The system has a pressure accumulator (I believe located next to the fuel filter), which is supposed to maintain system pressure after the car has been shut off. If it isn't working, then system pressure is leaking down and isn't high enough to keep the car running when you start it.

When you turn the key, the fuel pump starts running, and if you wait a couple seconds you are giving it time to build up system pressure again and, voila!, the car starts and runs fine.

GregS
'84 300D
'90 300CE