My 95 did similar. Ended up being the sway bar bushings and a shock on the front finally giving up the ghost...
Everything was great until about 50 then the slight tremor in the steering.. Reminded me of a tossed weight. Then at about 55-60 mph it would occasionally vibrate almost like a death wobble but it didn't have the shift feel to it.. It felt like the tire was bouncing up and down. Which is what it was doing...
On another rig the issue was it sat in flood waters for short time then was left to sit for a few months before i got it... Half of the front left rotor was severely rusted and caked with flood mud. it would have a constant out of balance feel in the steering even with new tires... Didn't discover it until I replaced the front brake components.

 

Front U joints can be mis installed, causing misalignment of the shafts. Vibrates like crazy around 60. The snap rings all have to be on. Personal experience on this one and the factory service manual mentions it also.

 

I had this problem right after installing a new set of Cooper Discoverer AT3 load range 4S on my XJ. One tire required 4 balance weights to balance it, but it ran straight and true on the balancer with no heave. On the front, it shook hard at 55 mph, but cleared up at 60 mph. I put it on the rear and I only got a slight tremor at 55-60 that cleared up at 65. Next time I'm buying only P-rated ones. DON'T buy the 10-ply ones! They are rated for duelies. I've run 4 sets of these tires on my WJ (P-rated) with no problems.