1985 BMW 535 6 cyl Two Wheel Drive Manual 260k miles
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my 85 bmw manual tranny 6 cyl. with 260,000 mi. runs great other than this sound. I bought this car aftr it had been sitting for over a year it wasnt running i replaced the battery and changed the oil it started right up accelerates well downshifts smoothly engine is as quiet as the desert. Now the prblem is when im driving and accelerate eveythings good but right when i lay off the gas i hear this noise that sounds like a flat which it obviously is not. i cant pinpoint where the sound is coming from but somwhere under the car more central im guessing. I dont think its transmission because my shifting and downshifting is smooth maybebe drivetrain differential or fuel firing i dont know it literally sounds like a flat tire.It makes it when i lay off the gas and slows in sound as i slow in speed whether im in gear or in neutral coasting.

This could be drive shaft, or subframe bushings or a wheel bearing. Put the car up on a lift and inspect.