FLC OF AN LTT JET EXPERIENCED AN ENG FLAMEOUT DURING CLB IN HIGH ALT. A SUCCESSFUL RELIGHT OF THE ENG WAS MADE AT THE APPROPRIATE ALT.

Narrative

IN CRUISE AT FL350; ATC CALLED FOR A CLB TO (WRONG WAY) FL370. CLB PWR/PERFORMANCE AND ENG INSTS WERE NORMAL. AT PLUS OR MINUS FL364; IN CALM AIR; R ENG QUIT. (THIS HAS HAPPENED MANY TIMES TO OUR G.E. CF700 AND CJ610 ENGS; BUT I STILL HATE IT WHEN THAT HAPPENS!) I TOOK CTL OF THE ACFT; INITIATED SINGLE ENG 'DRIFT DOWN;' TOLD ATC WE NEEDED 'LOWER;' CALLED FOR RELIGHT CHKLIST. (TOP OF RELIGHT ENVELOPE IS FL300 AND THAT'S WHERE RELIGHT WAS INITIATED.) RELIGHT WAS SUCCESSFUL AT PLUS OR MINUS FL290. WE GOT CLRNC BACK UP TO FL310; AND WE WENT ON TO SHV; OUR INTENDED FUEL STOP. BECAUSE WE WERE LIGHT AND WITHIN EASY RANGE OF SEVERAL SUITABLE ALTERNATES; I DIDN'T CONSIDER THE SIT AN EMER. (I'VE DECLARED SEVERAL EMERS -- I'M NOT BASHFUL ABOUT DOING SO.) DOUBTLESS; ATC GOT SOME TFC OUT OF OUR WAY. AT SHV; I CALLED OUR DISPATCHER AND THE MAINT SHIFT SUPVR ON DUTY. THEY VOICED NO OBJECTION TO MY CONTINUING THE TRIP; AT OR BELOW FL350. (WE FLEW FROM SHV TO MMLO TO ELP; MUCH OF IT AT FL350 -- NO PROBS.) LATER; I WAS INFORMED THAT THE ACFT SHOULD'VE BEEN GNDED FOR AN INSPECTION AT SHV.