Very likely bad torque and thrust links on the rear, both sides. They have vulcanized in place rubber bushings that contribute to the spring rate, so when they fail, the springs are "soft".

Bad rear shocks will also make the car wallow.

Get the front end aligned at a shop that understands Benz -- if you do not pre-load the front tires while setting the toe, they will have too much toe-out and the car will wander all over the place.

Ditto for tie rods, idler arm bushings, and drag link -- any play there and you get funky steering and excessive tire wear. No vibration to speak of.

Peter

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1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!