What was found
ON DESCENT WITH A/T ENGAGED, FELT/HEARD ENGINE SURGE/STALL. DISENGAGED A/T AND UPON MANUAL APPLICATION FWD AND AFT OF THRUST LEVERS, HEARD FELT SURGE/STALL. ENGINE PARAMETERS REMAINED NORMAL AND WERE BEING MONITORED ON DESCENT. THE FLIGHT MADE AN UNEVENTFUL LANDING. DURING MX TAXI TO THE HANGAR, THE NR 1 ENGINE FUEL FLOW WAS FLUCTUATING SLOWLY BETWEEN 700 AND 800 LBS/HR. WHEN THE THRUST LEVER WAS ADVANCED SLIGHTLY, THE ENGINE STARTED TO SHAKE/VIBRATE WITH SUBSEQUENT ANNUNCIATION OF THE ENGINE FAIL MESSAGE AND THE ENGINE SHUTDOWN. ACCOMPLISHED FIM 71-05 TASK 805 AND SUBSEQUENTLY FOUND THE 5TH STAGE CHECK VALVE STUCK OPEN. THE VALVE WAS REPLACED. THE GROUND ENGINE RUN WAS NORMAL AND THE AIRPLANE RETURNED TO SERVICE.