Rear end noise
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I just bought a 2000 f150. It makes a strange noise too. The noise that you might be hearing, might be the E brake shoes. If thay have not been touched or have been in mud. When they dry and the rust starts the thin shoes will fall apart. Check your brake shoes. If the truck has a posi, it is possible that the clutches are worn. That would be the next thing to check. O by the way when you said the axles move, did you mean in and out or front to back. If front to back then it is a axle bearing. A little in and out is normal.