POTENTIAL CONFLICT IN FOREIGN AIRSPACE.

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OUR FLT WAS GIVEN DSCNT CLRNC FROM FL370 TO FL310. TCASII ALERT CAME ON AT ABOUT FL317. MOMENTS LATER WE HAD A TCASII RESOLUTION COMMAND OF 'CLB XING CLB.' FO STARTED A CLB AND AFTER HEARING 'CLR OF CONFLICT' LEVELED OFF AT 32500 FT. WE DID NOT SEE THE TFC UNTIL IT PASSED OFF TO THE L AT APPROX FL310; TOKYO CTR WAS NOTIFIED OF TCASII DEV. WE THEN VERIFIED CLRNC FOR DSCNT TO FL310. SUPPLEMENTAL INFO FROM ACN 271494: DURING DSCNT FROM 370- 310 WAS ADVISED BY TOKYO CTL TO EXPEDITE DSCNT 'TFC AT FL330.' PASSING FL320 WAS ALERTED BY TCASII CLB' RESOLUTION. WAS RELUCTANT TO CLB DUE TO PREVIOUS TA. AIR MASS WAS CLR AND ONLY TARGET INFO ON THE TCASII SCOPE WAS A 'PLUS' AT 11 O'CLOCK. RESOLUTION DISPLAY CONTINUED TO MOVE ON L EDGE OF TCASII SCOPE SHOWING ONLY 'PLUS.' CLB ADVISORY CONTINUED. DISPLAY MOVES OFF L EDGE OF DISPLAY SHOWING '00 PLUS.' I CLBED IMMEDIATELY; TARGET CAME INTO SIGHT 10 O'CLOCK; 3-4 MI. CLB PEAKED AT 32500 FT. SUPPLEMENTAL INFO FROM ACN 271499: ACFT WENT OFF L WING AT ABOUT 5 MI SAME ALT. TYO CTR WOULD NOT ADMIT TO PROB.