RPTED LOSS OF SEPARATION BTWN RPTR'S MD11 DSNDING TO 6000 FT AND ANOTHER ACR AT 6000 FT.

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HOLDING INBOUND TO TOKYO'S NARITA ARPT AT ARIES INTXN AT 8000 FT. INBOUND COURSE IS 258 DEGS L TURNS; 7 MI LEG. AFTER TURNING INBOUND WE WERE GIVEN A CLRNC TO CONTINUE OUR TURN TO HDG 160 DEGS AND DSND TO 6000 FT. A FLT BELOW US HAD A PREVIOUS CLRNC TO DEPART ARIES ON A HDG OF 160 DEGS AND WAS AT 6000 FT. AS WE ROLLED OUT ON THE 160 DEG HDG AND DSNDED BELOW 6500 FT; WE RECEIVED A TCASII TA ALERT AND REALIZED THAT THE OTHER FLT WAS NOW CLOSELY IN TRAIL AND TRACKING PARALLEL TO US. WE LEVELED OFF AT 6200 FT WITH A -200 INDICATED ON THE TA ALERT. THE OTHER FLT WAS LESS THAN 1 MI TO OUR 4-5 O'CLOCK POS. ATC WAS ADVISED AND THE OTHER FLT WAS DIRECTED TO TURN R TO A HDG W OF OUR TRACK. THE COPLT COULD SEE IT OVER HIS SHOULDER AND THE FLC ACKNOWLEDGED SEEING US. APPARENTLY ATC MISJUDGED THE RESULT OF THE 2 DIFFERENT CLRNCS GIVEN EACH FLT. MY CONCERN IS WHY WE NEVER GOT A TCASII RA ALERT EVEN THOUGH WE WERE WITHIN 200 FT ALT AND LESS THAN 1 MI PROX TO THE OTHER ACFT. OUR TCASII HAD TESTED OK AND WE WERE GETTING ALT INFO FROM THE OTHER ACFT.