BMW Repair: BMW E30 316i shakes randomly, bmw e30, bmw 316i

Question
Hi there!
Im from sweden so it's a little bit hard to describe the problem but i'll try my best.
The car is a BMW 316i 1989.
Sometimes when i press the gaspedal the car shakes and is having a hard time acceleratin. The shake is quite suttle but noticiable.
It doesn't always do this though, it mostly does it when im accelerating to 60-70mph, stop accelerating and when i try to accelerate again the problem occurs. I have changed oil, fuel and airfilters.

Answer
Joakim,
 Its hard to tell exactly what the problem is, but it sounds like ignition problems.  I would replace all the ignition components if they have not been replaced in the last few years.  This includes:  Spark plugs, Plug wires, Distributor cap and rotor button.  Sometimes the Coil is replaced as well
 Good luck,
 Josh