Narrative:

We departed ZZZ, to return to ZZZ1 under part 91. We are a part 135 operator. But the flight in question was an empty non revenue leg home to ZZZ1. During the climb to cruise altitude, we encountered clear air turbulence at FL370 and the right engine flamed out. We then informed ATC of the situation. We did not declare an emergency. We descended to the relight envelope and restarted the right engine. Then began a new climb to our filed altitude of FL410. At FL400, the right engine flamed again. We advised ATC of the failure. Advised that we needed to descend to the relight envelope to relight. Again, we did not declare an emergency. ATC asked if we needed assistance, and we said no. We restarted the engine and climb to FL330 and changed destination to ZZZ2. We landed and purchased fuel. I advised my employer of the situation. We then flew from ZZZ2 to ZZZ1 at 17500 ft, well within the relight envelope. Upon arrival, I grounded the aircraft per our operation specifications. At the time of this writing, I'm waiting for maintenance's analysis of the engine. I was flying pilot on both ZZZ to ZZZ2 occurrences. Callback conversation with reporter revealed the following information: the reporter stated maintenance made several checks and then replaced the engine fuel control. On test flight the engine performed ok. The reporter is uncertain if the clear air turbulence actually caused the first flame out.

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Original NASA ASRS Text

Title: A LEAR25 IN CLB AT FL370 HAD THE R ENG FLAME OUT. DSNDED AND SUCCESFULLY RESTARTED ENG. CLBING THROUGH FL400, THE R ENG FLAMED OUT AGAIN.

Narrative: WE DEPARTED ZZZ, TO RETURN TO ZZZ1 UNDER PART 91. WE ARE A PART 135 OPERATOR. BUT THE FLT IN QUESTION WAS AN EMPTY NON REVENUE LEG HOME TO ZZZ1. DURING THE CLB TO CRUISE ALT, WE ENCOUNTERED CLEAR AIR TURB AT FL370 AND THE R ENG FLAMED OUT. WE THEN INFORMED ATC OF THE SIT. WE DID NOT DECLARE AN EMER. WE DSNDED TO THE RELIGHT ENVELOPE AND RESTARTED THE R ENG. THEN BEGAN A NEW CLB TO OUR FILED ALT OF FL410. AT FL400, THE R ENG FLAMED AGAIN. WE ADVISED ATC OF THE FAILURE. ADVISED THAT WE NEEDED TO DSND TO THE RELIGHT ENVELOPE TO RELIGHT. AGAIN, WE DID NOT DECLARE AN EMER. ATC ASKED IF WE NEEDED ASSISTANCE, AND WE SAID NO. WE RESTARTED THE ENG AND CLB TO FL330 AND CHANGED DEST TO ZZZ2. WE LANDED AND PURCHASED FUEL. I ADVISED MY EMPLOYER OF THE SIT. WE THEN FLEW FROM ZZZ2 TO ZZZ1 AT 17500 FT, WELL WITHIN THE RELIGHT ENVELOPE. UPON ARR, I GNDED THE ACFT PER OUR OP SPECS. AT THE TIME OF THIS WRITING, I'M WAITING FOR MAINT'S ANALYSIS OF THE ENG. I WAS FLYING PLT ON BOTH ZZZ TO ZZZ2 OCCURRENCES. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED MAINT MADE SEVERAL CHKS AND THEN REPLACED THE ENG FUEL CTL. ON TEST FLT THE ENG PERFORMED OK. THE RPTR IS UNCERTAIN IF THE CLEAR AIR TURB ACTUALLY CAUSED THE FIRST FLAME OUT.

Data retrieved from NASA's ASRS site as of July 2007 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.