This problem is most often caused by ground loops. The best way to fix it is to ground everything (head unit, amps, etc.) to the exact same point. If one of your units is connected to the factory ground that existed for your original head unit and the other is grounded somewhere else (as is typically done) it could be your problem. They should both be grounding to the same place. Do you have an external amp? If so, it should also be grounded to the exact same place.

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1982 Mercedes-Benz 300CD
1982 Mercedes-Benz 240D - stick