Narrative:

Level at FL390 with occasional light turbulence tank to engine fuel feed #1 ignition on. Aircraft weight 555000 pounds. We experienced a sudden jolt and #2 engine began to unspool. Within 30 seconds #3 engine began to unspool. First officer requested lower altitude, captain was flying. The first officer and I began the engine shutdown checklist. After engine shutdown all engine parameters appeared normal so we began the restart procedure. Both engines restarted with no problems before we reached FL300. We then requested FL350 and continued to hkg with no further incident.

Google
 

Original NASA ASRS Text

Title: 2 ENG FLAME OUT ON A 4 ENG ACR WDB ACFT AT HIGH ALT CRUISE.

Narrative: LEVEL AT FL390 WITH OCCASIONAL LIGHT TURB TANK TO ENG FUEL FEED #1 IGNITION ON. ACFT WT 555000 POUNDS. WE EXPERIENCED A SUDDEN JOLT AND #2 ENG BEGAN TO UNSPOOL. WITHIN 30 SECONDS #3 ENG BEGAN TO UNSPOOL. FO REQUESTED LOWER ALT, CAPT WAS FLYING. THE FO AND I BEGAN THE ENG SHUTDOWN CHKLIST. AFTER ENG SHUTDOWN ALL ENG PARAMETERS APPEARED NORMAL SO WE BEGAN THE RESTART PROC. BOTH ENGS RESTARTED WITH NO PROBLEMS BEFORE WE REACHED FL300. WE THEN REQUESTED FL350 AND CONTINUED TO HKG WITH NO FURTHER INCIDENT.

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.