Badger: good advice so far. Just to add to Bruce's advice: IF you had taken the drive shaft apart, and then reinstalled it without having marked it, that might be a contributing factor, or if a PO or mechanic had done it, that m-i-g-h-t be the cause. On another note: I noticed that you said "while accelerating up a hill in 4th gear or in OD...": uphill is NOT the place to be in 4th or OD, you are asking the engine to do something that it cannot do, at least not without straining it, and your transmission. Shift from OD to 4th, and then to 3rd, and then to second if need be. Machines are a compromise between power and speed: 4th gear/OD are speed, 1-2-3 are for power. And finally, my '86 745 (auto trans) had the same type of vibration, between +/-55 and 70, and it had my mechanic baffled, having gone thru balancing, rotating, etc., the tires. I let him be baffled, and I let myself suffuse my discomfort/worry over potential problems. Finally, it was time for new brakes, rotors and tires. Again, after balancing, etc., same thing: 'bad' vibes, ESPECIALLY when braking at high speed. I asked him to rotate and balance the tires one more time: VOILA! no more problem! Now I KEEP the left front tire where it is, and only rotate the right-side tires. That may not be the best thing in the world, but I can live with it. You may have a similar remedy. So far, I am happy to be driving vibe-free, and if it only costs me a tire every 30 or 40,000 miles, I'll be a happy camper. --PD.