Possibly the wheel bearings
You did not say what year it was, and that makes a difference. But you can check these things--- U-joints in front drive shaft, Front CV joints and axel shafts.
Rear wheel drive: Possibly a worn universal joint on the drive shaft. Front wheel drive: possibly worn CV joints on the front drive shafts.
You need to check the u joints at the front wheels.
Front drive axle joints bad
The hormone that makes a pregnant woman have their joints unstable is Relaxin.
sounds like you need to replace the U-Joints in the drive shaft
The company that makes the Grand Cherokee is the American company Chrysler, they produce it under the JEEP division. They have been making the Grand Cherokee since 1983.
You need to check the u joints at the front wheels
Assuming it is front wheel or 4 wheel drive, it is worn CV or Constant Velocity Joints. :o)
Check the rear drums, make sure nothing is broken in there, I was having the same problem and that's what it was...
Makes them move better
Dry ball joints/suspension joints. Universal joints going bad. Worn brake pad "squealers".