FLC OF ACR WDB ACFT DECLARED EMER WHEN 3 OF ITS 4 ENGS LOST PWR AT HIGH ALT CRUISE.

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CRUISING AT FL410; HAZY SKY; OUTSIDE AIR TEMP -63 DEG F; #4 ENG STARTED TO DECELERATE (ALL INDICATORS; EPR; EGT; N1; FF) FUEL HEAT ON; ALL IGNITION ON; 2 AND 3 FUEL X- FEEDS OPENED. ENG STARTED TO RECOVER THEN STARTED TO DECELERATE AGAIN AND STARTED TO RECOVER AGAIN. #1 ENG STARTED TO DECELERATE: TURNED OFF 3 PACK. CALLED SFO ARINC FOR LOWER ALT FOR WARMER AIR; POSSIBLE RELIGHT IF FLAMEOUTS AND BETTER CTL OF ACFT. ARINC SAID TO STANDBY WHEN SECOND ENG SHOWED INSTABILITY. I DECLARED AN EMER; TURNED OFF TRACK 90 DEGS TO S AND AT 25 NM STARTED TO DSND. AT TOP OF DSCNT #3 ENG STARTED TO DECELERATE. AS WE PASSED THROUGH FL370 THE AIR BECAME MUCH WARMER AND ENGS STARTED TO STABILIZE. AT FL330 ENGS BECAME STABLE. ARINC CLRED US DIRECT TO SFO AND AT 127 DEG W WE CONTACTED ZOA ON VHF. #3 ENG SHOWED SOME SIGNS OF INSTABILITY AS PER A PREVIOUS WRITE-UP. ADVISED CTR ALL ENGS APPEARED TO BE STABLE AND WE WOULD CONTINUE DIRECT SFO. MAIN TANKS HAD AT LEAST 10000 POUNDS FUEL IN EACH TANK. FUEL PRESSURE NORMAL THROUGHOUT EVENT. ANOMALY: WHEN #3 PACK TURNED OFF; CABIN TEMP BECAME VERY COLD. #1 PACK WAS TURNED OFF AND 3 PACK TURNED ON AND CABIN TEMP RETURNED TO NORMAL. FLT ATTENDANTS WERE BRIEFED ABOUT SITUATION AND IT WAS AGREED THAT NO FURTHER ACTION WAS REQUIRED UNLESS ENGS STARED TO HAVE PROBLEMS AGAIN. CABIN WOULD BE SECURED EARLY TO FACILITATE RAPID PREPARATION IF IT BECAME NECESSARY. ALL CREW MEMBERS HANDLED SITUATION WELL AND PERFORMED THEIR ASSIGNED TASKS WITHOUT DIFFICULTY. BEFORE WE LEFT SHA WITH ACFT ON GND THERE WAS A HVY RAINSHOWER. AFTER TKOF WE PASSED THROUGH A LINE OF LIGHT TO MODERATE RAINSHOWERS. BAL OF FLT WAS SMOOTH. WHEN IT BECAME LIGHT; SKY HAD A DUSTY; HAZY APPEARANCE; BUT NO ACRID ODOR IN COCKPIT OR CABIN. STANDARD FUEL HEAT PROCS WERE USED AND IRREGULAR PROC FOR 'ABNORMAL ENG RESPONSE TO THROTTLE MOVEMENT' WAS FOLLOWED. LANDED IN SFO.