MD11 AND B777 MEET HEAD ON AT ASSIGNED ALT ON A590 IN THE PACIFIC. ATC ADMITS ERROR.

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FLT X WAS OPERATING EBOUND FROM RJBB TO ZZZ. ON DEC/XA/99; FLYING ON AIRWAY A590; A W TO E RTE; AT FL310; DAY VFR CONDITIONS. AT PINSO WAYPOINT; FL330; WAS REQUESTED FROM ZAN AND APPROVED. FLT X CLBED TO FL330. APPROX 1/2 WAY BTWN PINSO AND PIPPA WAYPOINTS; THE FO NOTICED A TCASII ACFT SYMBOL ABOUT 30-40 NM AHEAD OF FLT X WITH AN ALT DIFFERENCE OF ZERO. THE FO DECREASED THE RANGE ON THE NAV DISPLAY AND DETERMINED THAT THE TCASII SYMBOL WAS INDEED A CONVERGING TARGET; ALSO APPARENTLY CRUISING ON AIRWAY A590 AT THE SAME ALT AS FLT X BUT IN A WESTERLY DIRECTION; OPPOSITE OF THE 'FLOW ARROW' SHOWN ON COMMERCIAL CHART (HI) 1/2. THE FO THEN INFORMED ME OF THIS AND I DECREASED THE SCALE ON THE NAV DISPLAY TO MATCH HIS AND AGREED THAT THE TARGET CLOSURE SPD WAS HIGH AND THAT THE OPPOSING FLT WAS AT THE SAME ALT. AT NEARLY 20 MI; THE ACFT WAS VISUALLY ACQUIRED; SLIGHTLY ABOVE AND SLIGHTLY TO THE R OF FLT. AT APPROX XB50Z THE TCASII WARNED 'TFC; TFC.' SHORTLY THEREAFTER; THE WARNING CHANGED TO 'CLB; CLB.' THE FO CHANGED HIS NAV DISPLAY TO TCASII. I STAYED IN MAP MODE; AND WE BOTH AGREED AN AVOIDANCE MANEUVER SHOULD BE EXECUTED. I DISCONNECTED THE AUTOPLT AND COMMENCED THE CLB; EVEN THOUGH WE HAD VISUAL ACQUISITION ON THE CONVERGING ACFT. THE FO NOTIFIED ZAN OF OUR ACTIONS. THE OTHER ACFT; BELIEVED TO BE FLT Y; ALSO INFORMED ZAN THAT THEY HAD AN ACFT IN SIGHT; CLOSE; AND IN THE OPPOSITE DIRECTION. AFTER GAINING 700 FT ALT AND GETTING CONFIRMATION FROM TCASII OF BEING 'CLR OF ACFT' WE RETURNED FLT X TO FL330 AND INFORMED CTR. JUDGING BY THE PRESENTATION ON THE NAV DISPLAY; I WOULD GUESS THE 2 ACFT PASSED WITHIN 2-3 MI OF EACH OTHER. HOWEVER; BASED ON VISUAL ACQUISITION AND THE RELATIVE SIZE OF THE ACFT; I WOULD GUESS THE SEPARATION TO BE 1-2 MI; AND I WOULD CLASSIFY THIS INCIDENT AS A 'CLOSE ENCOUNTER' RATHER THAN A NEAR MISS. SUPPLEMENTAL INFO FROM ACN 458912: LOCATION: 197 NM E OF ONEIL INTXN. GOING DIRECT; I RETURNED TO THE COCKPIT FROM MY BREAK ABOUT 1 HR PRIOR TO THE INCIDENT. WE HAD BEEN CLRED FROM SOMEWHERE OVER THE GULF OF ALASKA DIRECT TO ONEIL INTXN. ABOUT 197 NM FROM ONEIL AT FL330 THE CAPT STATED THAT WE HAD A TARGET AT OUR ALT; A LITTLE OVER 20 MI OUT. SHORTLY THEREAFTER; TCASII GAVE US TFC ALERT. WE SPOTTED THE ACFT ABOUT 10 MI OUT. THE CAPT BEGAN A TURN TO THE L SINCE THE TFC WAS OFFSET SLIGHTLY TO THE R. THE TCASII THEN GAVE US AN RA. WE WERE VISUAL ON THE OTHER ACFT AND TURNING AWAY ALREADY. THE OTHER ACFT HAD BEGUN A SLIGHT CLB. THE ACFT (WE THINK IT WAS THEIR ACFT X) PASSED LESS THAN 3 MI AWAY AND 300 FT ABOVE OFF THE STARBOARD SIDE OF OUR ACFT. OUR TRACK TO ONEIL WAS APPROX 257 DEGS MAGNETIC. THE APPROX LOCATION WAS 5550N 17740E. TOTAL CONTACT WITH THE X WAS ABOUT 1 MIN. WHEN WE ASKED ATC ABOUT THE CONFLICT; THEIR ONLY RESPONSE FROM THE FEMALE CTLR WAS 'IT WAS A MISTAKE.' IT APPEARS THAT X WAS EBOUND ON TRACK A590.