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I have a 1999 Jeep Grand Cherokee V8 with 325,000 miles. Lately when I reach 55 MPH I get a shake or hesitation. It feels like it is in the drive train and not an engine problem. I also notice that when I make a hard low speed turn (into the garage) the steering wheel shakes hard). Any ideas??? Other than this problem this vehicle looks and runs like new, when I took it to the shop they "guessed" it may need a new transfer case.  

They are right. It happened to mine too. The transfer case needed to be replaced. I got a used one installed for $950 but it too started to do the same thing after a while.

Also the Brake discs are prone to warping with this model so watch for a shimmy while braking at higher speeds too. It'll get progressively worse until it is terribly obvious.