Car won't move & clunk in rear

1996 4Runner V6 4x4 with automatic transmission & 135K miles. I believe it has a limited slip rear end. About 1 time per week when I put the car in drive it won’t move. I give it some gas (about 1500 rpms), it feels like it is trying to move but won’t until there is a clunk in the rear & then car drives without problem. There is no problems with slippage of the transmission, even when going up hills or acclerating. Problem only occurs in drive, not in reverse. Only occur when starting from a stop. A few times on snow or ice one rear tire will spin & the other feels like it is dragging (not rotating). Transmission fluid is fine & changed as suggested in owner’s manual. Thanks

On ice or snow, if you do not have limited slip traction, one tire drives the truck and the other doesn’t. I think you DO have this feature, since you would not notice the unpowered rear wheel unless you did, or unless the brake caliper was stuck (forcing the brake on that wheel to be engaged all the time). The clunking noise is the key. Your first repair should be to replace the u-joints. If that does not help, the rear axle needs repair.

I wouldnt replace the u-joints just yet. My thinking is there is slack in the rear end and it get "bound up? and or noises in the drive train can travel…maybe its binding forward of the rear end and when it comes lose your hear the bang in the rear end from the sudden drive to the rear. Its a thought…

But Peacefrog, the first place slack and binding would occur is the u-joints, right? They are designed to fail first and easily, to prevent damage to the rest of the drive train. It’s an easy and cheap repair, and it should be eliminated first as the cause of the clunking sound. I agree that it gets dicey after that, but I would start with the most obvious and cheapest option first.
I think having the front and rear u-joints replaced by a shop should cost around $100.

Thanks for the information. This happen again the other day. I looked out at the rear tires as I slowly put on the gas, the rear tires started to rotate a few degrees. Then the clunk occured & the car moved as if nothing were wrong. The passenger rear wheel bearing was replaced about 15K miles ago.
I also thought about the brake getting stuck. Front disc & rear drum. This happen even when we don’t use the emergency brake.

I wouldn’t rule a transmission problem out just yet. Even if the fluid was changed every 30k miles as it should be keep in mind that the internal seals in the transmission are rubber, 16 years old, and the characteristics of rubber changes a lot with age.
Point being that the clunk may only be a normal symptom of another problem altogether.

A sticking brake caliper could also cause something like this.

To me it sounds like you have a brake problem rusting to the rotors or drums.