BOTH ENGS OF A LEAR JET LR24 UNSPOOLED TO FLT IDLE AFTER A FEW MINS OF CRUISING AT FL430 CAUSING THE FLC TO DECLARE AN EMER AND DSND TO FL220 BEFORE BEING ABLE TO REGAIN NORMAL PWR OUTPUT. SINCE THE ACFT WAS NOT BEING PRESSURIZED DUE TO INSUFFICIENT ENG BLEED AIR; THE FLC AND PAX PUT ON THEIR OXYGEN MASKS. FLC DIVERTED TO LAND.

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WE WERE FLYING AT FL390 AND WE WERE PICKING UP LIGHT TO MODERATE TURB. WE ASKED ZLA FOR FL430 AND THEY APPROVED IT SO WE CLBED UP TO FL430. WE WERE LEVEL THERE FOR ABOUT 10 MINS AND I ASKED THE CAPT WHAT THE RAM AIR TEMP WAS BECAUSE I NOTICED OUR MACH WAS FALLING OFF; HE REPLIED - 33 DEGS AND THEN HE PUSHED THE THRUST LEVERS UP. ABOUT 3- 4 SECONDS LATER THE R ENG ROLLED BACK AND WE ASKED CTR FOR LOWER. TO DO A RESTART THEY GAVE US FL280 AND WE WERE DSNDING ABOUT 30 SECONDS. AFTER THE R ENG ROLLED BACK THE L ENG ROLLED BACK TO ABOUT 15% EACH. THIS WAS ABOUT PASSING THROUGH FL400 AND FL390. AT THAT POINT THE CAPT TOLD ME TO TELL CTR THAT WE WERE DECLARING AN EMER; WHICH I DID. WE PUT OUR OXYGEN MASKS ON AS DID THE 2 PAX. THEIRS DEPLOYED AT 14000 FT CABIN ALT. AT ABOUT THAT TIME THE CAPT TOLD ME TO TELL CTR WE NEED LOWER AND THEY GAVE US 11000 FT. CTR ASKED US WHAT THE PROB WAS AND I TOLD THEM WE HAD A DUAL FLAMEOUT. ABOUT FL250 THE CAPT ATTEMPTED AIR START ON THE R ENG -- DID NOT WORK; SO HE DID A NORMAL START AND THAT WORKED. WE TOLD CTR WE HAD 1 ENG BACK AND WANTED TO CONTINUE TO LAS VEGAS; NV. THE CAPT GOT THE L ENG STARTED AT FL220 AND FL210. WE CONTINUED TO LAS VEGAS; NV; AT FL220 AND LANDED WITHOUT ANY PROBS. I THINK THE PROB WAS CAUSED BY THE FUEL COMPUTERS BEING OUT OF ADJUSTMENT; NOT ICE OR BAD FUEL BECAUSE WE NEVER GOT FUEL FILTER LIGHTS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT THE ENG DID NOT ACTUALLY FLAME OUT; BUT LOST PWR TO A FLT IDLE SO THAT UNTIL THE ACFT WAS DOWN TO A LOWER ALT IT WOULD NOT RECOVER DUE TO THE COMPUTER LACK OF PROPER ADJUSTMENT. THIS WAS ESTABLISHED AFTER THIS INCIDENT IN A FLT TEST PRIOR TO ADJUSTMENTS AND AFTER. THEY HAVE NOW BEEN ADJUSTED APPROPRIATELY AND FLT TESTED.