I have a vibration problem in my 1988 cadilac brougham rear wheel drive with 24,000 original miles.Put on 4 new cooper tires the car had 1987 vintage tires on. that didnot fix it the driveshaft had a dried out bushing that made it wooble and 2 new universals still did not fix it...also when you drive on the levelnthen start up a hill feels like it stays in high gear and doent want to shift well... any thoughts

Bent rims maybe or tires. I had a similar problem with two of my cars. One of them it was the tires,figured that one out when I sold the car & put the Original ones on. A second time I balanced my wheels & found out the rim was bent. By the way, some radials can not be rotated cross-wise just front to back on the same side. Hope this helped.

take the car to a suspension specialist shop and have the rear wheels aligned first
have the suspension checked for worn mounts or bad springs
it is very important that the rear end is aligned before the front end
suspect that the suspension rubbers need replacing as it is over 6 years old
the tyre rotation is a myth perpetrated on drivers to sell tyres
when the tyre construction was cross-ply and not radials yes rotation then on cross-ply tyres could get the wear to even out but with radials once the wear is started then the tyre continually wears in that pattern regardless of which wheel it is on
even if you take that tyre of the car and put it on a trailer , it will still continue to wear in that pattern
tyres are no longer rotated but simply put front to back on the same side other wise the belts flex in a new direction in the tread and fail earlier that expected
besides that fact that tyre rotation will not allow you to monitor for suspension problems or wheel alignment problems and cost you 4 tyres at a time instead of two

Check engine mounts. If it is a rear wheel drive or 4 wheel drive- inspect driveshaft(s) for damage or missing weights. Also check universal joints for wear, and the rear driveshaft slipyoke for leaks and wear. If there is a leak, the rear seal and bushing should be replaced.

If front wheel drive, inspect drive axles for damage, and inspect the steering components for damage or wear.

Here is the basic maintenance list for your Jeep:

~ Inspect lights and check tire pressure at least monthly or before & after each trail ride

~ Oil & filter change, chassis lubrication, differential and transfer-case fluids every 3,000 to 5,000 miles or 3 to 4 months - if you have recently crossed through water deep enough to submerge the centre of your hubs, replace the differential fluids as a precaution

~ Underhood belt and hose inspection every 3,000 to 5,000 miles or 3 to 4 months (every oil change)

~ Tire rotation and wheel balancing every 6,000 miles or every other oil change - driving offroad can knock wheel weights off a wheel, so you may need to have this done more frequently

~ Brake inspection every 6,000 miles or every other oil change - if you have rum brakes in the rear, ensure they are cleaned after each trail ride where you encountered deep mud/snow

~ Replace air filter every 12,000 to 24,000 miles or as indicated by inspection - dusty trails can shorten these intervals dramatically

~ Replace fuel filter every 24,000 to 100,000 miles

~ Automatic transmission service every 24,000 to 100,000 miles

~ Wheel alignment check every 12,000 to 24,000 miles or as indicated by tire wear - offroad driving can knock wheels out of alignment, so budget for an alignment every 3 months, then watch tread wear to see if it's needed

~ Cooling system flush and refill every 40,000 to 100,000 miles

~ Belt and hose replacement every 60,000 to 100,000 miles or 5 to 8 years

~ Engine timing belt replacement every 60,000 to 100,000 miles (when equipped) or 5 to 8 years

~ Air conditioning performance check annually, usually in the spring - be sure to run your A/C during the winter for brief period to ensure all hoses and valves stay lubricated and operable

Check the u- joints are fitted in line, if ok check wheel balance both front and rear.

caster,camber and, wheel bearings
have your car 4 wheel aligned this will adjust your rear caster and, camber.
have your wheel bearings checked

I would guess incorrectly tightened or installed wheel bearing. Or it might just need to get greaced.

it could be as easy as checking to see if you have a dented rim.....

or as expensive as changing the "constant velocity joints" but only if it is a front wheel driven car.....

how are your shocks?

have they repacked the rear bearings..."but only if not rear wheel driven car"

Replace all your fluids including the gas. Even if the gas looks good it can still be bad and will make the car run horrible. Oil needs to be changed just sitting everything has broken down same with tranny fluid. Change the tires and check the suspension and the shocks. Very nice car though. Just do the normal maintance on it. Filter, oil, tranny fluid, spark plugs, tires normal

Most shimmies come from tire/wheel/balance combos. Before your dollars go down on 4 tires(assuming you have good tread), rotate tires & if there is a change you can figure out the offending unit