ACFT DRIFTS DOWN AND TURNS OFF COURSE AS 2 ENGS FLAME OUT. EMER DECLARED.

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SIMULTANEOUS FLAMEOUT OF ENGS #1 AND #4. ACCOMPLISHED 'RAPID ENG RESTART' CHKLIST. ENG #4 STARTED ON FIRST ATTEMPT. ENG #1 STARTED ON SECOND ATTEMPT. FUEL PANEL CONFIGN WAS MAIN TANKS #2 AND #3 FEEDING ALL 4 ENGS. CTR OVRD/JETT PUMPS OFF/SCAVENGE PUMP ON. HAD BEEN IN THE CONFIGN ABOUT 10 MINS. FUEL HEAT WAS OFF. ALL INDICATIONS WERE NORMAL. DECLARED EMER; TURNED OFF TRACK; LOST 1200 FT BEFORE ABLE TO RESTART ENGS AND RETURN TO ALT AND COURSE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: ALTHOUGH RPTR WAS NOT IN THE FLT DECK WHEN ALL OF THIS HAPPENED; HE WAS ABLE TO SEE THE PROCEDURAL STEPS TO RESTART THE ENGS. HE RPTED THAT FUEL FEED FROM TANKS WAS PROPER AND NOTHING WAS DONE TO INDUCE THE ENGS TO FLAMEOUT. MAINT CHKED ALL FUEL SYS ELECTRICAL WIRING AND FUEL SUPPLY LINE VALVES. EVERYTHING WAS CHKED ON THE GND TO BE WORKING PROPERLY. CAPT AND FO SPENT SOME TIME IN THE SIMULATOR REVIEWING THE FLAMEOUT SCENARIO. RPTR WAS NOT IN THE FLT DECK SO HE WAS NOT INVITED TO PARTICIPATE IN REVIEW. THERE WAS A CHK AIRMAN ON BOARD IN THE FLT DECK AND HE SAW NO PROCEDURAL ERRORS BY THE FLC. RPTR COULD OFFER NO EXPLANATION OF WHY THE ENGS FLAMED OUT.