It could also be that someone forgot a shim when they replaced an axle. That one is easy to check. Grab each axle with the car on level ground in neutral and try to move the differential end in or out. If its missing a shim you will be able to hear the axle clunk as it slides in and out. It also happens when the differential is unloaded when decelerating.

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1985 300 TD 448K
1984 300 TD 278K

1983 240D euro 240k
1994 f-250 idi turbo 330K
1986 f-350 IDI
1987 F-350 IDI

1985 JD 1050 4wd
1965 IH 3660