FLC OF A B757 DSNDED BELOW ASSIGNED WHEN THE ACFT STARTED A HIGH ALT STALL DURING LEVEL FLT AT FL410. UPON EXECUTING THE HIGH ALT STALL RECOVERY; THEY WERE ABLE TO MAINTAIN FL370 TO WHICH THEY WERE RECLRED.

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WE HAD BEEN CRUISING AT FL410 FOR APPROX 30 MINS IN DAY; SMOOTH; UNLIMITED VISIBILITY WX. WINDS FROM W AT 66 KTS. OVER INTL WATERS. MACH .793 DURING FIRST 15 MINS. DILIGENTLY WATCHED HOW AIRPLANE WAS PERFORMING (NEAR MAX CRUISE ALT). GOT INTO CONVERSATION WITH FO; OCCASIONALLY OBSERVING INSTS BUT NOT OVERLY CONCERNED ABOUT OUR STATUS; SINCE WE WERE IN A STRAIGHT AND LEVEL; CLR; SMOOTH ENVIRONMENT. FELT A SHUDDER AND BOTH OF US OBSERVED AIRSPD AT APPROX 185 KTS; LEVEL; WITH ENGS PRODUCING MAX CRUISE PWR. DISCONNECTED AUTOPLT; AUTOTHROTTLES; APPLIED FULL PWR; AND BEGAN SLOW DSCNT (HIGH ALT STALL RECOVERY PROC. AT FL408; FO ASKED AND RECEIVED CLRNC TO FL350 FROM CTR. BY FL375; ACFT BACK ON CRUISE SPD AND REQUESTED FL370 AS NEW CRUISE ALT. NO EMER DECLARED. ACFT TYPICALLY IS +/-15 KTS OFF AIRSPD IN NORMAL CONDITIONS. I HAVE APPROX 300 HRS PIC WITH PREVIOUS 800-1000 HRS FO TIME OVER 10 YRS. FO HAS 3 YRS IN TYPE. I DIDN'T FEEL I WOULD HAVE DONE ANYTHING DIFFERENTLY AT CRUISE. I CAN ONLY FIGURE THAT A GRADUAL TEMP INCREASE MUST HAVE OCCURRED WHEN AIRSPD WAS 5 KTS SLOW AND ACFT SLOWLY WENT TO MAX CRUISE WITH AIRSPD CONTINUING TO DECREASE WITH NEITHER OF US NOTING A SERIOUS CONDITION BUILDING.