B757-200 CREW AND A DC9 HAD LESS THAN LEGAL SEPARATION IN TNCF NON RADAR AIRSPACE.

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RA IN UNCTLED AIRSPACE. FLT WAS LEVEL AT 15000 FT. TCASII ALERT WITH ONCOMING TFC; 12 O'CLOCK POS; DSNDING FROM ABOVE WITH HIGH CLOSURE RATE. TCASII BECAME A TA; THEN RAPIDLY BECAME AN RA. WE GAINED VISUAL CONTACT WITH ACFT AT ABOUT 5-6 MI. RA STATED MONITOR VERT SPD AS ACFT DSNDED THROUGH OUR ALT; THEN RA GAVE US A CLB. THIS CAME SO FAST WE WERE UNABLE TO RESPOND BEFORE TCASII WENT FROM RED TO YELLOW TO WHITE. ESTIMATE ACFT PASSED BELOW AND SLIGHTLY R AT ABOUT 500 FT WITH A CLOSURE RATE OF 800 KTS. CURACAO CTL HAD A LONG CONVERSATION IN SPANISH WITH OTHER ACFT. WE GOT ACFT INFO/CALL SIGN XXXX HAD BEEN CLRED PLT'S DISCRETION FL280 TO FL260. INSTEAD; HE CONTINUED ON DOWN TO 10000 FT; PASSING THROUGH OUR ALT. SUPPLEMENTAL INFO FROM ACN 534675: DEPARTED ARUBA AND HAD BEEN LEVEL AT 15000 FT FOR A FEW MINS WHEN WE RECEIVED A TA ON THE TCASII DEPICTING AN ACFT ABOUT 5-10 MI AT 12 O'CLOCK POS; 1200 FT ABOVE; DSNDING. IN VMC; WE ACQUIRED THE ACFT VISUALLY; JUST TO THE R OF 12 O'CLOCK POS; CLOSING AND DSNDING TOWARD OUR ALT. THE TA IMMEDIATELY BECAME AN RA; COMMANDING 'MONITOR VERT SPD.' A MOMENT LATER THE RA CHANGED TO 'CLB' AS WE VISUALLY WATCHED THE ACFT PASS BY OUR STARBOARD SIDE; DSNDING THROUGH OUR ALT. THERE WAS ABOUT 1 SECOND FROM THE 'CLB' RA UNTIL THE ACFT PASSED US. WE DID NOT CHANGE ALT AS WE HAD INSUFFICIENT TIME TO REACT TO THE CHANGING RA PRIOR TO OBSERVING THE ACFT PASS US. ALTHOUGH VERY DIFFICULT TO ESTIMATE; THERE WAS APPROX 500 FT OF HORIZ AND LESS THAN 500 FT OF VERT SEPARATION. WE RPTED THE EVENT TO CURACAO CTL AND THEY REPLIED THAT THE OTHER ACFT WAS CLRED TO DSND FROM FL280 TO FL260 AND CONTINUED THE DSCNT TO 10000 FT WITHOUT CLRNC. THIS IS A NON RADAR ENVIRONMENT AND THE ONLY WAY THAT THE CTLR CAN DETERMINE ACFT POS IS BY RECEIVING RADIAL AND DME RPTS FROM APCHING AND DEPARTING ACFT. SUPPLEMENTAL INFO FROM ACN 534674: APPROX 100 MI N OF ABA ON UA567 AFTER DEPARTING AUA; WE GOT A TA THEN AN RA TO MONITOR VERT SPD; THEN SHORTLY THEREAFTER A CLB RA. DSNDING DC9 WAS ACQUIRED VISUALLY AT APPROX 10 MI WHEN FIRST RA WAS COMMANDED. IT PASSED OUR ACFT ON R SIDE WITHIN APPROX 3-5 SECONDS OF CLB RA. DURING/JUST PRIOR TO THE RA; THE AUTOMATED VOICE COMMAND MADE AN INTERRUPTED COMMAND; ALMOST AS IF THE COMPUTER DID NOT KNOW WHAT COMMAND TO GIVE. ACFT LATERAL SEPARATION LOOKED TO BE BTWN 600-900 FT AWAY AND ABOUT 600 FT BELOW AS IT PASSED US OFF TO THE R. WE WERE LEVEL AT 15000 FT. CURACAO CTL TOLD US THE ACFT HAD BEEN CLRED FROM FL280 TO FL260. HE ALSO STATED THAT IT WAS ENRTE FROM SANTO DOMINGO TO ARUBA AND THAT IT WAS A DC9.