Check the rear suspension links for worn bushings. Any signs of cracks or shredding rubber means replacement -- I'd suggest torque, thrust, and camber links at least, probably better to do the tie-rods and spring arm bushings as well.

If the links are OK, check the subframe mounts for cracks -- if any are bad, replace all four.

Check differential mounts -- two at the rear end, one at the front. If the diff moves up and down independent of the subframe, the rear mounts are shot. You have to drop the diff down to replace the rears, so it's silly not to replace the front one at the same time (two rubber inserts).

And check the sway bar mounts -- if they are bad, the sway bar can rattle, although this isn't usually noticable on acceleration -- more an annoyance on rough pavement or speed bumps, were the sway bar the go "thumpa-thumpa thump) with a sort of ringing noise as the loose end bangs around. If only one end is loose, it will only happen when the opposite wheel is lifted.

Peter

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1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!