Back end moves sideways on acceleration or deceleration - 53 Chevy Tru

I have a 1953 Chevy truck with a 383 that I recently (several hundred miles ago)changed over from a Turbo 350 automatic to a Tremec TKO-500 5 speed with a hydraulic clutch.  The rear end is out of a 1972 camaro.  If I am cruising down the road at a constant speed and step on the gas to accelerate, the back end moves to the right (sort of fish tails).  Likewise if I am cruising in less than 5th gear and suddely take my foot off of the gas, the same thing happens in the opposite direction as I decelerate.  The problem was very slight at first, but seems to be getting worse.  Any suggestions on what the cause may be?  

Hey Chevytrapp,

Sounds like a classic case of worn leaf spring bushings.  I had a 70 chevelle that did the same thing, but it had actually wallowed out the holes in the control arm mounting points on the frame.  When you accelerate, or decelerate, it's letting the rear axle turn in relation to the truck.

Check all the spring shackles, bushings, and bolts, and also check the U bolts holding the axel to the leafspring.  You'll probably find one or more parts with some slop in them.

Hope that helps.

Good Luck!
Ace