my brother just had the same problem a couple months ago with his 94 325i... what it might be is the guibo, or flex disk(coupling) it has a thousand names but basically it is the rubber connector that joins the driveshaft and driveline. its relatively simple to replace if thats the problem. and if it is not the guibo its could be the center bearing that supports the driveshaft halves. now that would be a bigger problem and is something that would be done in a shop. to check these two things, remove the exhaust, remove the heat sheilds and at the very back of the transmission there is a big rubber donut with six bolts, inspect the donut-esk connector and if is ripped or torn thats your problem. if its the center bearing that is broken straight back from the trans there should be a bearing bolted to the underbody of the car and it could be broken.
check those out and go from there