A B777 PILOT REPORTS AN APU FIRE SUBSEQUENTLY EXTINGUISHED BY THE FIRE BOTTLE.

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PUSHBACK; TOWBAR; AND INTERPHONE DISCONNECT NORMAL. DURING ENG START; APU SHUT ITSELF DOWN; ACCOMPANIED BY CLACKING SOUND; AS IF A HARD XFER OF ELECTRICAL PWR TO IDG HAD OCCURRED. ENGS SPOOLED UP NORMALLY. EICAS MESSAGE: APU SHUTDOWN; STATUS MESSAGES: APU; APU CTL. FOLLOWING FLT MANUAL/ECL GUIDANCE; APU WAS RESTARTED. DURING APU RESTART; PUSHBACK CREW BEGAN TO WAVE AND POINT TOWARD THE TAIL OF THE ACFT. SIMULTANEOUSLY; ANOTHER ACFT CALLED ON RAMP CTL FREQ TO ADVISE WE HAD SMOKE AND FLAMES COMING FROM TAIL OF ACFT. I OBSERVED THAT APU SEEMED TO BE 'HUNG' AT 29% RPM AND 900 DEGS C EGT. I MOVED APU SWITCH TO OFF. THE ADJACENT ACFT AGAIN RPTED SMOKE AND FLAMES FROM TAIL AREA. GND CREW CONTINUED TO WAVE AND POINT. FO INQUIRED IF HE SHOULD PULL APU FIRE HANDLE. I CONCURRED. FO PULLED FIRE HANDLE AND DISCHARGED FIRE BOTTLE. ADJACENT ACFT THEN RPTED FLAMES EXTINGUISHED. ACFT WAS THEN TAXIED BACK INTO GATE FOR MAINT ATTN. WHILE WAITING FOR MAINT INSPECTIONS; APU OIL QUANTITY STATUS MESSAGE APPEARED. THIS WAS NOT ADDRESSED; SINCE APU WAS TO BE DEFERRED. MAINT FOUND NO EVIDENCE OF DAMAGE IN APU AREA; OR EVIDENCE OF SMOKE/FIRE IN E&E COMPARTMENT. FLT WAS SUBSEQUENTLY DISPATCHED WITH APU INOP. COMPLETION OF FLT UNEVENTFUL.