This is a common problem for many Cadillacs, especially this model. I have had the tires balanced many times, the brake rotors turned, the axles replaced, the wheels (temporarily) changed out, all to no avail. My mechanic thinks it is the transmission, but estimates the cost to be $5000+. I think that it may be the front engine mount. Since the vibration isn't devastating to the car, I continue to drive it at lower speeds. I may just get an other car rather than putting more money into this one. I have been following several blogs about the situation and there hasn't been any definite solutions to the problem. Surprisingly (or not), Cadillac has been very quiet on the issue. For that reason alone, I wouldn't ever buy another Cadillac again. I like Lincolns much better.