Half accel. problem.

[Festively Jolly]

hello list.   the 1988 Audi 90 fwd has developed a new minor(?) problem.
it seems no matter the conditions (speed, gear, hot cold)  when the
accelerator is half way down the steering wheels shimmies and vibrates
and it is a noticeable feeling throughout the car.  it also makes a
"vibrating" noise.   it is kind of unpleasant.  but if i either let off
or give it more pedal, it stops and is just fine.  any thoughts?  thanks
allot!