I had the same problem with my '87 Olds 88, When I picked it up it ran a little rough but made the 200 mile trip home ok. Then it would hardly run, I posted it up on a GB American car forum and was told to get it scanned, replace the coil packs, my ecm was shot and the sensors had gone bad. I put new plugs & wires in and that fixed the problem immediately. I always treat any car I buy to a full service and checkover anyway so no extra expense was involved.
Always check the easiest fix first before you start throwing money at the car.
Thanks for letting us know what you found and fixed the problem.
Roger.

Had the Same issue on my 92 Bonneville. Replaced the Fuel Filter (Loooong overdue)...when I pulled the filter out, the gas in it was Brown!!! (Sure sign there)

So it now has a New filter courtesy of Autozone and a small bottle of Lucas Fuel Treatment in the gas tank...after about 10 or so miles of driving the shudder is almost unnoticeable. Next on my list is the PCV Valve.