86 5000CST stalls after first starting out

[Williams <jwms@hpe.infi.net>]

Hello list - I could sure use some help diagnosing the following
problem.

My '86 5000CST with 177K miles starts and idles great, but after driving
1 mile down the road, the car always stalls when taking the foot off the
gas pedal to apply the brakes for a stop sign.  The car will start back
up and run/idle great again.  It usually doesn't stall again until the
car is parked for an hour or so and then the whole thing starts over.

The car dies just as if the ignition switch had been turned off - no
stumbling or anything like the usual symptoms of a vacuum leak.  I have
recently replaced most of the hoses under the hood to fix leaks which
prevented the car from idling at all.  The fuel mixture was also set
using the proper instrumentation.

Any suggestions on how to solve this problem would be greatly
appreciated.

Jim