AN ACR B747 RPTS THAT THEY HAD LTSS WITH ANOTHER ACFT WHILE CRUISING EBOUND OVER THE PACIFIC.

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AT APPROX XA20Z SEP/XA/97 I WAS CAPT AND PF FROM KIX TO LAX. WE WERE BTWN MJE AND UACKY AT FL350. A TCASII INDICATION OF AN ACFT APPROX 15 MI AHEAD AT THE SAME ALT COMING TOWARDS US APPEARED. WITHIN SECONDS WE GOT A TCASII TFC ALERT AND THE ACFT SYMBOL TURNED YELLOW. IT WAS APPROX ON OUR NOSE AND CLOSING. JAPAN ATC CALLED THE TFC TO OUR ATTN. I STARTED A DSCNT TO CLR THE TFC. WE WERE VFR; BUT IT WAS DUSK AND I HAD NOT YET SPOTTED THE TFC. I TOLD JAPAN ATC THAT I WAS DSNDING TO FL340. THE CTLR ADVISED THAT THE TFC WAS 'GOING IN THE OPPOSITE DIRECTION.' I DON'T UNDERSTAND WHAT SHE MEANT BECAUSE IT WAS GOING IN THE OPPOSITE DIRECTION AS WE WERE -- STRAIGHT TOWARD US. AS THE TFC WAS ABOUT TO PASS ABOVE US AND TO OUR R; A MALE CTLR CAME ON THE AIR AND TOLD US TO REMAIN AT FL350 AS THE TFC WAS GOING IN THE OPPOSITE DIRECTION. THIS WHOLE INCIDENT HAPPENED IN LESS THAN 60 SECONDS. WHEN THE MALE CTLR CAME ON; I WAS AT FL343 AS THE TFC WAS PASSING; SO I RETURNED TO FL350. THE ORIGINAL CTLR WAS DIFFICULT TO UNDERSTAND BY US AND OTHER ACFT. CLRNC REPEATS WERE COMMON. WE DID NOT HAVE TIME FOR A DISCUSSION.