I'm working on a '95 series 1 3800SC, with 92K miles. The supercharger coupling has a slight amount of "slop". It measures out at less than 1/16" side to side, or about 1mm, on the edge of the 2.8" pulley. It's off the vehicle, so now would be an easy time to replace it, but not sure if this is really bad or just "OK". Car will only see about 5K miles/yr going forward, so max of maybe another 50K.

I say while out of engine bay, it is much easier to replace the little stuff, like that and have piece of mind. water pump, back spark plugs, etc...

If the pulley is moving side to side then it might be the snout bearing. If there is play while rotating then its the coupler. It is easy to replace the coupler by draining the snout and removing the bolts. If the supercharger is on the bench, replacing the coupler is a 20 minute job. If there is play it will only get worse. I would replace it now.

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" THE BLACK PARALYZER" -87GT 3800SC Series III engine, custom ZZP /Frozen Boost Intercooler setup, 3.4" Pulley, Northstar TB, LS1 MAF, 3" Flotech Afterburner Exhaust, Autolite 104's, MSD wires, Custom CAI, 4T65eHD w. custom axles, HP Tuners VCM Suite.
"THE COLUSSUS"
87GT - ALL OUT 3.4L Turbocharged engine, Garrett Hybrid Turbo, MSD ign., modified TH125H
" ON THE LOOSE WITHOUT THE JUICE "

OK, I'll go ahead and replace the coupling. It is a rotational movement, not side to side. I can see the rotors engage as I spin it back and forth, so I'm sure it is the coupling. Just didn't know if any play was acceptable or not. Just didn't want to throw money at it if not necessary, but understand that it is a lot easier to do now than later ( same as the water pump). I'll also be doing the LIM gaskets as well.

Replace it.
I had no play at all and I replaced mine just as insurance as I knew nothing about the engine when I bought it, and couldn't hear it run.

This way you'll know it's good.

Peace of mind can be worth the money and effort you put in now,

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===Always trying to find time to work on cars===
Louis Duet
Baldwin, Long Island, NY
"My mind spins like helicopter blades." -G. Rossdale
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"Blue" <= '85 Fiero GT
3800sc series 2 swap in progress
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"Boo" <= '81 Delorean DMC-12
VIN #5835
Stock PRV engine
Peugot 604 Intake manifold
Exhaust headers
Anti-3rd brake light