Narrative:

At FL410 while in a left turn; we had a flameout on the left engine on a lear 25. Therefore; we could not hold altitude. We notified center 2 times that we had a flameout and needed to descend. They would not let us descend due to traffic. Then we declared an emergency. They gave us a right turn to 270 degrees at FL350. Then we told them we needed FL250; to attempt a relight and go to ZZZ1. They then cleared us to FL250. At FL250 we got a relight. They asked us if we would like to continue the emergency. We told them no; that we had both engines back and everything was normal. They gave us a right turn direct to ZZZ1. On the ground I called our head mechanic. He had me do a static run-up according to his specifications. Everything checked out normal. He cleared us to fly. We then went back up. At about XA30 at FL410 while in another left turn; we had another flameout of the left engine. We started to lose altitude. We notified ATC who cleared us to FL350. We told them we wanted to go to ZZZ2 and FL250 to attempt a relight. They cleared us direct and FL250. At FL250 we got the relight. We continued. The next day I talked to our head mechanic again and decided the best thing to do would be to fly home at FL250 which is in the relight envelope; so that maintenance could do a more thorough check.

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Original NASA ASRS Text

Title: AN LJ25 IN CRUISE FLT AT FL410 EXPERIENCED A FLAMEOUT OF L ENG. CREW DECLARED EMER AND DSNDED FOR A SUCCESSFUL RELIGHT. AFTER LNDG AND STATIC RUN-UP; THEY LATER HAD ANOTHER FLAMEOUT OF THE L ENG; AGAIN AT FL410.

Narrative: AT FL410 WHILE IN A L TURN; WE HAD A FLAMEOUT ON THE L ENG ON A LEAR 25. THEREFORE; WE COULD NOT HOLD ALT. WE NOTIFIED CTR 2 TIMES THAT WE HAD A FLAMEOUT AND NEEDED TO DSND. THEY WOULD NOT LET US DSND DUE TO TFC. THEN WE DECLARED AN EMER. THEY GAVE US A R TURN TO 270 DEGS AT FL350. THEN WE TOLD THEM WE NEEDED FL250; TO ATTEMPT A RELIGHT AND GO TO ZZZ1. THEY THEN CLRED US TO FL250. AT FL250 WE GOT A RELIGHT. THEY ASKED US IF WE WOULD LIKE TO CONTINUE THE EMER. WE TOLD THEM NO; THAT WE HAD BOTH ENGS BACK AND EVERYTHING WAS NORMAL. THEY GAVE US A R TURN DIRECT TO ZZZ1. ON THE GND I CALLED OUR HEAD MECH. HE HAD ME DO A STATIC RUN-UP ACCORDING TO HIS SPECS. EVERYTHING CHKED OUT NORMAL. HE CLRED US TO FLY. WE THEN WENT BACK UP. AT ABOUT XA30 AT FL410 WHILE IN ANOTHER L TURN; WE HAD ANOTHER FLAMEOUT OF THE L ENG. WE STARTED TO LOSE ALT. WE NOTIFIED ATC WHO CLRED US TO FL350. WE TOLD THEM WE WANTED TO GO TO ZZZ2 AND FL250 TO ATTEMPT A RELIGHT. THEY CLRED US DIRECT AND FL250. AT FL250 WE GOT THE RELIGHT. WE CONTINUED. THE NEXT DAY I TALKED TO OUR HEAD MECH AGAIN AND DECIDED THE BEST THING TO DO WOULD BE TO FLY HOME AT FL250 WHICH IS IN THE RELIGHT ENVELOPE; SO THAT MAINT COULD DO A MORE THOROUGH CHK.

Data retrieved from NASA's ASRS site as of January 2009 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.