A DASSAULT 20 ON A NEW #1 ENG TEST FLT HAD THE ENG FLAME OUT AT FL337 THE PNF INADVERTENTLY SHUT DOWN #2 ENG. BOTH ENGS RELIT AT FL290.

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CLBING OUT OF FL337 FOR FL350; I WAS IN THE L SEAT FLYING AND ANOTHER CAPT WAS WORKING THE RADIOS. HE HAD ALREADY ADVISED ATC THAT WE WERE DOING A MAINT FLT WITH A POSSIBILITY OF ENG LOSS REQUIRING A QUICK DSCNT. HE ADVISED NO EMER WOULD BE CALLED UNLESS WE LOST THE OTHER ENG. THE TEST ENG (#1) FLAMED OUT GOING THROUGH APPROX FL337. I STEADIED THE ACFT AND REACHED TO GUARD THE GOOD THROTTLE. BEFORE I COULD GET TO THE THROTTLE; THE OTHER PLT HAD SHUT DOWN THE GOOD ENG. I TOLD HIM HE HAD JUST SHUT DOWN THE GOOD ENG AND I CALLED FOR A SECURE CHKLIST TO PREPARE FOR A POSSIBLE RELIGHT. HE CALLED ATC; DECLARED AN EMER AND REQUESTED LOWER. ATC GAVE US LOWER; AND I PUT THE NOSE DOWN TO GET DOWN AND BUILD UP THE SPD FOR A RELIGHT. GOING THROUGH APPROX FL300; BOTH ENGS RELIT. WE STOPPED OUR DSCNT AT FL270 AND REQUESTED CLB TO FL290 TO COMPLETE THE ACCELERATION CHK. THE OTHER PLT CLRED THE EMER WITH ATC AND WE CONTINUED ON OUR FLT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE ACFT WAS BEING FLOWN TO TEST THE NEW ENG CHANGE ON THE #1 POS. THE RPTR SAID THE CAUSE OF THE FLAME OUT ON #1 ENG MAY HAVE BEEN IGNITION PROBS BUT WAS NOT CERTAIN. THE RPTR SAID THE EMER WAS CANCELED AFTER BOTH ENGS WERE RELIT AND THE TRIP CONTINUED.