MD11 CLBING WITH RPHI ARTCC EXPERIENCED TCASII RA AT FL295 WITH ENRTE ACFT; OPPOSITE DIRECTION ON SAME AIRWAY.

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WHILE CRUISING AT FL290; APPROX 10 MI S OF SAN VOR; WE WERE CLRED BY MANILA CTL TO CLB TO FL410. A FEW MINS EARLIER; WE WERE TOLD THAT OUR REQUESTED LEVEL OF FL330 WAS UNAVAILABLE DUE TO NBOUND TFC 20 MI AHEAD. WE WERE TRAVELING N ON B591 AT THE TIME. THEN MANILA CTL ASKED IF WE COULD ACCEPT A HIGHER LEVEL. AFTER CHKING PERFORMANCE INFO; WE REQUESTED FL410. A FEW MINS LATER; MANILA CTR CLRED US TO CLB TO FL410. WE INITIATED THE CLB VIA AUTOPLT THROUGH THE FMS. A FEW HUNDRED FT AFTER INITIATING THE CLB WE RECEIVED A TA; FOLLOWED IMMEDIATELY BY AN RA CALLING FOR A CLB. I DISCONNECTED THE AUTOPLT AND COMPLIED WITH THE RA. A FEW SECONDS LATER; THE RA CALLED FOR 'INCREASE CLB.' I INCREASED THE CLB RATE. AT ABOUT THIS TIME; THE ONCOMING ACFT ILLUMINATED HIS LNDG LIGHTS; APPEARING DIRECTLY AHEAD. AS THE INCREASED CLB RATE WAS APPLIED; THE RA CHANGED TO 'DSND NOW.' AT THIS POINT; I ROLLED R AND PUSHED THE NOSE OVER. SHORTLY AFTER THIS TURN; THE CONFLICTING ACFT PASSED TO OUR L AND ABOVE US. THE FIRST CALL FROM MANILA CTL CAME A BIT LATER WHEN THEY TOLD US WE WERE CLR OF THE TFC. THE OTHER ACFT THEN ASKED MANILA CTL TO CONFIRM THEY WERE IN RADAR CONTACT; MANILA DIDN'T ANSWER. I INITIATED THE R TURN IN ADDITION TO THE RA CLB THEN DSND COMMAND TO FACILITATE THE LOWERING OF THE NOSE; AND TO CLR THE AIRWAY. WITH THE ADVENT OF GPS; IT HAS NOT GONE UNNOTICED THAT TFC ALL TRAVELS PRECISELY DOWN THE AIRWAY DIMINISHING THE 'BIG SKY' EFFECT TO ALMOST NOTHING. I BELIEVE IT IS ONLY A MATTER OF TIME UNTIL 2 ACFT OPERATING ON THE SAME AIRWAY ARE INVOLVED IN A MIDAIR COLLISION. AFTER THE INCIDENT; WE CONTINUED TO FL410; BUT WE FAILED TO DON OUR OXYGEN MASKS. I ATTRIBUTE THIS TO OUR PREOCCUPATION WITH THE PRECEDING EVENTS. SUPPLEMENTAL INFO FROM ACN 597876: TFC WAS INDICATED ABOUT 5 MI AHEAD; 500 FT ABOVE AND CLBING; AND OPPOSITE DIRECTION. THE TFC PASSED ON OUR L SIDE BY APPROX 500 FT. WE RECOVERED AT ABOUT FL290 AND CONTINUED OUR CLB TO FL410. THE CREW FROM XXX ASKED IF WE WERE UNDER RADAR CONTACT; THE CTLR INDICATED YES; BUT GAVE NO OTHER RESPONSE. OTHER FACTORS THAT MAY HAVE CONTRIBUTED TO THIS EVENT: 1) TSTM LIGHTS ON (COCKPIT LIGHTS). 2) NAV DISPLAY AT HIGHER RANGE. 3) LANGUAGE BARRIER. OBVIOUSLY SHAKEN BY THIS EVENT; WE DID NOT DON OUR OXYGEN MASKS FOR THE PORTION OF THE FLT AT FL410.