B747-200 CREW ENCOUNTERED SEVERE MOUNTAIN WAVE ACTIVITY NEAR GRF IN ZLC CLASS A AIRSPACE.

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CRUISING AT FL410 NEAR GREAT FALLS. I WAS PF AND FLYING ON AUTOPLT. ENCOUNTERED UNRPTED MODERATE TO SEVERE MOUNTAIN WAVE; WORST THAT I HAD EVER EXPERIENCED. AIRSPD DROPPED OFF ABRUPTLY; ADDED PWR AND AIRSPD IMMEDIATELY ACCELERATED TO (AND PAST) BARBER POLE. TOOK AUTOPLT OFF; AND RETARDED THROTTLES. AIRSPD DROPPED PRECIPITOUSLY. DURING THIS EVOLUTION; PITCH ATTITUDES WERE VARYING BTWN 3 DEGS NOSE DOWN AND 7 DEGS NOSE UP IN AN ATTEMPT TO MAINTAIN FL410. KEEPING WITHIN THESE PARAMETERS REQUIRED VERY AGGRESSIVE PITCH MOVEMENT. DURING THIS TIME; ACTUAL INDICATED ALT VARIED BTWN FL408 AND FL413.5. MACH VARIED BTWN .78 MACH AND .88 MACH; ALTHOUGH THE SO THOUGHT THAT HE SAW MUCH SLOWER. AS ENGS WERE SPOOLING DOWN IN RESPONSE TO RETARDING THROTTLES; AIRSPD DROPPED QUICKLY AND THROTTLES WERE ADVANCED. ENG #1 EXPERIENCED A STALL CONDITION AND WOULD NOT RESPOND TO THROTTLE INPUT IN EITHER DIRECTION. CAPT IMMEDIATELY RPTED THE MOUNTAIN WAVE; ALMOST SIMULTANEOUSLY WITH 2 OTHER ACFT RPTING SAME. WHEN ENG #1 WOULD NOT ACCELERATE (IT HAD STALLED AT IDLE); CAPT IMMEDIATELY ASKED FOR LOWER ALT. INITIALLY ASSIGNED FL370. APCHING FL370; ENG STILL WAS NOT RESPONDING; SO ASKED FOR LOWER STILL. ASSIGNED FL330. DURING DSCNT; #1 THROTTLE LEFT AT IDLE. LEVELING OFF AT FL330; ATTEMPTED TO ADVANCE THROTTLE AND ACCELERATE ENG. ENG BEGAN TO RESPOND NORMALLY. FLT CONTINUED UNEVENTFULLY TO MSP. CREW WROTE UP LOGBOOK ENTRY; AND FILED OUT ENG OP RPT. NO INJURIES IN CABIN DURING EPISODE.