Subaru AWD rear-wheel "judder"

I have an intermittent problem with my 2002 AWD Outback wagon. Occasionally, while driving at highway speed (with cruise control on), the rear wheels “judder” vigorously (violently?)-- I feel like I am driving on the rumble strip on the side of the interstate. There is no pulling , the vehicle tracks perfectly straight. Upon pulling over to the side of the highway and shutting off the car, and starting out again, the symptom remained. So, pulled over again and shut car off, then restarted engine, the problem went away.

The previous owner (my father in law) had the same problem 4 years ago, and the dealership replaced the differential. Curiously, the dealership claimed the car must have been towed in on 2 wheels, while my father in law claims (and I have every reason to believe him) that the car was carried to the shop on a flatbed tow truck with all 4 wheels on the bed.

I realize that intermitent problems are by their nature hard to diagnose, but any advice would be greatly appreciated.



There are other ways to screw up that differential, but towing it with one set of wheels on the ground would certainly do it. Putting different tyres on the front than on the back can also do it.

The car has the same tires front and back, the inflation values are within 1.5 psi of each other-- I hope that is not too great a difference-- and, I have no reason to believe the PO ever had the car towed with one set of wheels on the ground (either with the old differential or the new differential installed by the dealer). What puzzles me is that it happens rarely, and at highway speeds, and there is no indication that it’s about to happen. All is fine until it happens.