ACR X TRACK DEV DUE TO TCASII TA DISPLAY OF TFC. POSSIBLE LTSS. POSSIBLE SYS ERROR.

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ACR X ENRTE MIA-GIG CRUISING FL330 SBOUND NEAR CARACAS; VENEZUELA. FO NOTICED OPPOSITE DIRECTION TFC AT OUR ALT ON TCASII. BEGAN A L TURN TO INCREASE LATERAL SEPARATION. ALT READOUT ON TCASII SHOWED OTHER ACFT CLBING AND WAS RELIEVED WHEN ALT INCREASING THROUGH FL352 WAS NOTED BUT STILL CONCERNED ABOUT WHAT WAS BELIEVED TO BE POOR SEPARATION. OTHER ACFT REACHED FL355 AND BEGAN DSNDING. OUR TURN INCREASED TO 90 DEGS OFF COURSE AT MAX BANK ANGLE. ABOUT THIS TIME A TA WAS ANNUNCIATED ON THE TCASII. MEANWHILE; THE FO WAS ADVISING CTL OF OUR DEV AND THE REASON. CTL RESPONDED WITH A LENGTHY XMISSION BUT QUALITY WAS SO POOR THAT CTL WAS UNREADABLE. THE BITS AND PIECES UNDERSTOOD SEEM TO ADD UP TO THE FACT THAT OUR CTLR WAS NOT CTLING OTHER ACFT AS OTHER ACFT DISAPPEARED ON TCASII THE LAST ALT INDICATED WAS FL328. IT IS JUST A GUESS BUT IT APPEARED THAT THE OTHER ACFT WAS CLRED TO CLB AND THEN GIVEN AN IMMEDIATE DSCNT BUT WITH THE DELAY IN COMS IT ONLY EXACERBATED THE SIT. THE ESTIMATED CPA AT FL330 FOR BOTH ACFT IS 5 NM. I AM NEW TO SOUTH AMERICAN FLYING AND WHILE I HAVE BEEN ADEQUATELY BRIEFED ON POTENTIALS FOR CONFLICT IN THIS AIRSPACE; THIS INCIDENT MAKES IT VERY CLR. KNOWING THAT IT ONLY TAKES ABOUT 20 SECONDS FOR CLOSURE AT 5 NM; I WILL NOT HESITATE TO DEVIATE FROM ANY SIT THAT DOESN'T 'LOOK RIGHT' AND WILL NOT WAIT FOR A TA AS WAS DONE IN THIS CASE. FURTHER; REGARDLESS OF HOW LATE THE HR AND QUIET AND LONELY IT SEEMS OUT THERE; I WILL CONTINUOUSLY MONITOR THE TCASII (ALONG WITH EVERYTHING ELSE).