My Dad has a 1996 Jeep Grand Cherokee with about 102,000 miles & at any speed (not every time) if you tap the brakes, the front end starts to shimmy & is difficult to get it to quit. I thought it might be the steering stabilizer shock. It was safety inspected a short time ago with no problem or loose parts found. Any ideas? Thanks

You need to install a heavy duty stabalizer shock and ditch the stock one. Then if you still have it your front tires are shot and it doesn't matter how much tread is on them. You can try to balance and rotate, but the solution for me was brand new all terrain tires, smooth as silk since then.

I would say that you have WARPED DISC BRAKE ROTORS which is the beginning and possibly all of your problem. It he suspension such as STRUTS are weak, that will elevate the problem. Hope this helps.