I agree with A264172. I had that problem with a car once and when I had the car out for a road test during a Pre Purchase Inspection, the mechanic pointed at the engine mounts right away. I have also heard from many W124 owners that they changes their engine mounts. The previous owner of my car had them replaced before I bought the car.

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1989 300CE Astralsilber/Schwarz
1992 300CE Schwarz/Schwarz