What was found
NR 1 ENGINE FLAMED OUT AT FL350, NO INDICATION FOR REASON WHY. INSPECTED FUEL FILTERS, BOROSCOPED AND VISUALLY INSPECTED ENGINE, NO DEFECTS FOUND. R & R FUEL PRESSURE VALVE, OPS AND LEAK CHECKED GOOD. PERFORMED GROUND RUN, NO DEFECTS NOTED. TEST FLIGHT OF ACFT UNSATISFACTORY, ENGINE FLAMED OUT AT FL 350. R & R FUEL CONTROL UNIT, OPS AND LEAK CHECKED GOOD. ALL WORK PERFORMED IAW MM SEI 187. SECOND TEST FLIGHT OF ACFT UNSATISFACTORY, ENGINE FLAMED OUT AT FL 346. ENROUTE, CREW REPORTED THE ACFT SHUDDERED, APPEARED TO BE COMPRESSOR STALLED. MX R & R NR 1 ENGINE FUEL PUMP IAW SEI-187 MM 73-13-0. OPS AND LEAK CHECKED GOOD. NR 1 ENGINE OVERSPEED GOVERNOR FAILED BYPASS CHECK. R & R NR 1 ENGINE OVERSPEED GOVERNOR IAW SEI-187, MM 73-23-0. LEAK AND OPS CHECKED GOOD. ACFT TEST FLOWN AND ENGINE PASSED ALTITUDE ACCELERATION CHECK AT FL350.