BMW Repair: 1987 BMW 325is Problem, 1987 bmw 325is, bmw 325is

Question
When I give the BMW gas it drops below idle RPM almost stalling and then proceeds to accelerate.  Do you have any idea what this could be?

Answer
Hi Travis!
Run the engine at idle, open the hood and look at the throttle valve linkages, see if the accelerator cable moves the throttle valve smoothly when opening and closing, then check the vacuum hoses connecting to the throttle valve and idle air valve and intake manifold for leakage/wornout spots.
If your complaint is accompanied by rough idling (which you did not mention), there is a probability that you have a bad idle air valve and/or leaking vacuum hoses.
You may also have to check the fuel pressure while actively trying to duplicate the stalling and then acceleration.
Other than these, you also  have to consider ignition problems (like timing which should be checked by a timing light). Old cars like yours oftentimes have wornout distributor components. But remember that timing is controlled by the DME (engine control module) and is not adjustable manually. A long shot but still a possibility is a wornout timing chain.
You have to work at each possibility one by one. It is not easy and I sympathize with you. But that is the price you pay for loving an old vehicle.
Tino