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Hi - I've reviewed the threads in the forums and seen similar problems to mine, but nothing that's really an exact match, so I'm posting this.
Quick background: have a 93 LT1 that I store every winter. This last winter, it was stored for about 2 years with me starting it up and letting it run every couple months. I used gas stabilizer in a full tank during storage.
Problem: Took the car out, ran fine except for a new "bucking" or "stuttering" when in 6th gear at low rpm (about 1500) and on the gas hard. The bucking was about every 2 or 3 seconds, not too bad.
Put in some Gumout "fuel system cleaner" with 1/3 of the old gas still left. Then filled up with new 93 octane. The bucking seemed to get a little worse. Under 1/2 or more throttle, the bucking started up in any gear at any rpm. With 1/2 tank of gas gone, added one more bottle of Gumout injector cleaner. Tank now down to 1/8 left (of what should be new gas) and no better...
...except when the engine is cold. If the engine is cold, there are absolutely no problems. It runs fine. The bucking only starts once the engine is heated up and running. And it's only under acceleration. During idle at a stop light or while cruising (engine hot or cold), the car runs fine.
Could be bad wires. HEI ignition cars like ours are very sensitive to them. Open your hood at night or in a darkened garage, pull the hood lamp fuse, then start the engine.
Look for telltale arcing and electrical "creepycrawlies" along your plug and coil wires. If you see any, replace all the wires with new ones. The O.E.M. Delco/Packard wires are good for 60,000 miles, then they should be replaced.
My '92 did the same thing your car is now doing and it turned out to be the wires.
My 92 will do this when i have the traction control on so thats the first thing i do is turn it off try that and see if it helps. if not i would say its some kind of electrical problem or maybe fuel pump going out.