THE FLC OF A B747-400 FLYING OVER THE NORTH PACIFIC NOTICE AN ACFT FLYING BELOW THEM ON THEIR TCASII DISPLAY AT FL310. THE LOWER ACFT STARTS TO CLB AND THE FLC ASSUMES THEY ARE GOING TO FL330; HOWEVER; THE LOWER ACFT CLBS THROUGH FL330 AND STARTS INTO FL350. RPTR TAKES EVASIVE ACTION; BUT NEVER RECEIVES A TCASII RA. AS THE OTHER ACFT APCHS FL350; HE EVIDENTLY SEES RPTR'S ACFT AND DSNDS TO FL330 IMMEDIATELY.

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ENRTE WITH TOKYO RADIO AT FL350; ACFT BELOW US WAS CLRED TO FL330 (WE DID NOT HEAR THE CLRNC). WE NOTED HIS INITIAL CLB ON TCASII. WE RECEIVED A TA SHOWING 400 FT SEPARATION AND AN 'UP ARROW' INDICATION. AT THAT POINT I DISCONNECTED THE AUTOPLT AND WENT INTO A CLBING L TURN. THE ACFT WAS VISIBLE BELOW US ON THE L; DSNDING. WE REACHED AN ALT OF FL356 AND BEGAN A DSCNT TO FL350. MUCH AS I MALIGNED THE ORIGINAL TCASII SOFTWARE; I THINK IT MAY HAVE SAVED A MIDAIR IN THIS CASE. APPARENTLY; IN MY ESTIMATION; THE OTHER CREW MISSET THEIR INTENDED ALT IN THE CTL PANEL AND WERE IN FACT CLBING TO OUR ALT (WHICH WE HAD BEEN AT SINCE NATES). THIS FORM HAS BEEN IN MY BAG FOR 15 YRS; BUT I THINK THIS IS AN IMPORTANT INCIDENT. IT SHOWS THE DANGER OF MISSETTING THE INTENDED ALT ENRTE (SINCE I ASSUME THEY NEVER RECEIVED ANY WARNINGS UNTIL THE TA) AND POSSIBLY THE NEED FOR TA AND RA TRAINING IN SIMULATOR SESSIONS (AS I MADE WHAT WAS; BY OUR COMPANY MANUALS; A WRONG DECISION AND MANEUVERED AWAY IN A 2000 FT AIRSPACE SEPARATION SIT WITHOUT AN RA). THERE WERE NO OTHER CONFLICTS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES THAT THEY SAW THE ACFT ON THEIR TCASII LEAVE FL310 AND ASSUMED IT WOULD LEVEL AT FL330. WHEN IT KEPT ON CLBING UP INTO RPTR'S ALT; HE TURNED THE ACFT TO MAINTAIN A VISUAL CONTACT WITH IT. THE OTHER ACFT MADE VISUAL CONTACT WITH RPTR'S ACFT AND MADE AN IMMEDIATE DSCNT TO LOWER ALT. RPTR ASSUMES THE ALT LIMITER WAS NEVER SET IN THE CONFLICTING ACFT COCKPIT. THERE NEVER WAS ANY RADIO COM BTWN THE 2 ACFT. EVEN TOKYO RADIO NEVER SAID ANYTHING SO TOKYO ARTCC WAS NEVER AWARE OF ANY POSSIBLE CONFLICT. RPTR GIVES CREDIT TO TCASII FOR PREVENTING A MIDAIR COLLISION. THEY WERE NAVING BY GPS WHICH IS HIGHLY ACCURATE. BECAUSE MORE ACR'S ARE USING GPS FOR NAV; RPTR BELIEVES AN ALTDEV IS MORE DETRIMENTAL AS AN ACFT ASCENDING INTO ANOTHER ACFT WILL HAVE NO LATERAL SEPARATION. ANY VERT MOVEMENT WILL ALWAYS BE DIRECTLY INTO ANOTHER ACFT IF THERE IS NO IN TRAIL SEPARATION. THE OTHER ACFT WAS A B747 FROM A FOREIGN FLAG.