I have a prob and need some help. My 93 325is on acceleration seems to speed up then slow down then speed up then slow down, on and on without me ever releasing the gas pedal. This problem has been there since I had it and I had the exact same problem with my 86 E30. Help me please its driving me crazy.

well 93 had traction control, that might nbe the cause but if ur 86 e30 had the same thing maybe its time to replace o2 sensors? It would be good to hear more info on the car milage, auto/5spd transmission, what ger its in if 5spd etc.

Fuel filter, injectors need cleaning,injector leaking, fuel pressure regulator faulty.
Fuel pump delivery volume low. Coolant temp sensor faulty. Intake system leak.

Any fault codes?
Water in gas could give these results try a little isopropyl alcohol or other water scavenger and see if it clears up.
Seems unlikely given that this appears to be somewhat rhythmic, but it's the cheapest on the list of problem sources.
Water would cause rough running at speed.

If not, look at the other areas I've suggested.

No traction control, tried o2 sensor, problem in all gears. 93 325is with 5spd, 93k original milage. The problem is on full acceleration.

I have same problem before but since I changed O2 sensor it gone.

Changed o2 sensor in other car to no avail..