I have a 92 loyale 100,000mi 3sp a/t. While driving I have noticed this sound in the front end. I am driving say 55mph and let off the gas real slow you here a thumping sound or when you slowly press on the gas you here it. If you keep the gas pedal in one area it will do it. Does not do this when you apply the brakes or when you driving along normal speed. It seems to do it for a few seconds when you let off or get on the gas. Also last year put a new axel on drivers side. It seems to do it when Iam doing 65 and slow down to 55. thump thump thump and quits.

engine/transmission mounts, engine torquing when you gas or decelerate and hitting something. i've heard of engines hitting the hood when engine mounts go out.

 

check bolts - tire lug nuts and axle nuts for tightness.

 

is this an AWD? if so i'd inspect the ujoints of the driveshaft. best to remove and inspect unless you're really good at inspecting them on the car. off the car a bad ujoint will look terribly bad or just feel very "lump" when you move it by hand.

The DOJs can do funny things also.