A B737-300 ON AUTOPLT DURING DSCNT ONE ENG THROTTLE CAME BACK ALMOST TO IDLE. PUSHED THROTTLE UP TO REGAIN SPD. HEARD 'THUD' WROTE UP ITEM. ON GND AIRPLANE REMOVED FROM SVC.

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CAPT FLYING ON AUTOPLT. GIVEN DSCNT TO FL310. DURING DSCNT; THROTTLE CAME BACK TO ALMOST IDLE AND SPD GOT A LITTLE SLOW. PUSHED THROTTLE UP TO REGAIN THE SELECTED SPD AND AFTER ABOUT 1/2 INCH OF THROTTLE MOVEMENT; HEARD A THUD THROUGH THE ACFT. WE WERE BUSY WITH DSCNT AND WITH NO ABNORMAL ENG PARAMETERS NOTED; CONTINUED. AFTER LNDG; WE WROTE UP THE THUD WE HEARD AND MAINT TECHNICIAN MET ACFT AND DEBRIEFED WITH US. THEN TOOK ACFT OTS WITH SUSPECT COMPRESSOR STALL. TOOK ACFT TO HANGAR AND THEY DID SOME CHKS AND I GOT ANOTHER CALL IN MY HOTEL MAINT NEEDED TO GET MORE INFO. I THEN BRIEFED WITH HIM AND I SAID AND THAT IT REALLY SHOULD BE TEST FLOWN TO SEE IF THEY COULD DUPLICATE THE PROB AS MY FO NOR MYSELF HAD EVER SEEN OR HEARD THIS. IN ABQ; HAD ANOTHER MAINT PROB AND CALLED MAINT AND ASKED WHAT HAPPENED TO THIS ACFT. HE SAID IT TEST FLEW AND THEY WERE ABLE TO DUPLICATE BUT THIS TIME THE ENG FLAMED OUT. (THE THUD WE HEARD SOUNDED LIKE A PERSON FALLING; BIRD STRIKE; CART SLAMMING INTO THE GALLEY; ETC.)