Rear Brakes make thumping noise

'95 Mustang GT
When I press my brakes ir feels like the rear brakes make a thumping noise? What could it be?
Also the car starts to vibrate on excelleration (right around 60mph), it's not a tire out of alignment shake (the steering wheel doesn't shake) the whole car has a vibration to it.
Thanks Hi: For the brake problem, you might have a shoe wearing uneven that may be caused by a bad wheel cylinder. At any rate, a visual check should be performed on the rear brakes.

You vibration problem could be a u-joint going bad. If you 'stang is a manual transmission, look at the rear u-joint (closest to the rear end. If it's an automatic, look at the front u-joint (nearest the transmission). Took to my mechanic and found out the drive shaft bolts were almost completely unscrewed. After screwing them back in, no problems...drives like it's brand new!!! Hi: Wow. You were lucky no to have lost the driveshaft somewhere on the highway, causing serious problems Car Repair Talk's forum.