It could be the rear differential, but that wouldn't be my first thing to check. Could also be in the rear driveshaft.

I would look first to the transfer case. A loose chain will cause a similar noise. Another item to check is the front driveshaft yoke where it joins the transfer case, that is a common failure point that can create a similar noise. It is caused by wear due to insufficient contact on the sliding yoke. There are fixes for this one that don't require replacing the transfer case (which is sometimes suggested as the solution).

Any of these could be diagnosed by having the vehicle on a hoist (safely) and shifting forward/reverse while listening underneath. This must be done safely. It can be difficult to determine if the noise is front or rear from the driver's seat, and the most common cause is actually amidships.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
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