it could be a fuel pump problem, but i've encountered same problem of trying to get more speed but only rocking back and forth with the car. i got it fixed by replacing the spark plugs, and distributer cap and plugs. this fixed the problem. the car is shaking because its not receiving the power that it needs. hope this helps have a 1988 535i with 156000 miles. After the car seems to warm up the acceleration becomes very jaggedy. I will accelerate and it will go smooth than get clogged then break loose again.