I have a 86 SE with a 3.4l pushrod engine and 3 speed auto trans that has a vibration when accelerating. It's bad between 2000-3000 rpm. I've replaced the axle shafts, checked transmission mounts and engine mounts, control arm bushings. Ball joints and tie rods are all good. Does the transmission have support bearings for the axle shafts? The left axle seems to have a good amount of up and down play. It's driving me crazy!

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88 Coupe: 2.0L Turbo 4 Cylinder, W2A, T25 Turbo.
84 Indy #64: Restoration Project, Super Duty 4 swap

If your axles wiggle more than about 1/8th of an inch as you push and pull them, chances are the output bearings are bad. I had that happen to my Getrag....and I think the auto has the same design, but probably a different bearing. What I noticed first was a noise like a small 2 engine airplane makes when the engines are out of sync. If nothing happens when you rev the car in neutral, the engine is okay.