ACR AT CRUISE HAS TCASII RA REGARDING CLBING TFC.

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FLT GRU (SAO PAULO; BRAZIL) TO MIAMI. NBOUND LEVEL AT FL390 BASICALLY IN CLR AIR BUT SOME CIRRUS ON UA315. 50 MI S OF ALBOG INTXN; OUR TCASII SAID 'TFC; TFC.' TCASII SCREEN SHOWED TFC 12 O'CLOCK; 800 FT BELOW US AND CLBING! WITHIN SECONDS IT WAS 500 FT BELOW US AND TCASII SAID 'DSND XING; DSND NOW!' I TURNED THE AUTOPLT OFF AND LOWERED THE NOSE UNTIL THE IVSI WAS IN THE GREEN AT +/- 1200 FPM DSCNT. IVSI SHOWED 'RED' FROM 1000 FPM UP TO 1000 FPM DOWN (2 GREEN LIGHTS WERE AT 1100 FT AND 1200 FT APPROX DOWN). FO TURNED ON ALL LIGHTS AT THIS SAME TIME. I TURNED THE ACFT R AT THE LAST MOMENT BECAUSE WE FINALLY SAW NAV LIGHTS OF THE OTHER ACFT AT OUR 11:30 POS. AS THE ACFT PASSED US IT APPEARED TO BE ABOUT 1 MI OR LESS L OF US AND TCASII SHOWED HIM 100 FT ABOVE US. WE THEN NOTIFIED MAIQUETIA CTL AND FLT SUPPORT OF THE NEAR MISS/RA FROM TCASII. THE COMMON AIR-TO-AIR FREQ TO MONITOR IN THIS LOCATION FOR ALL FLTS ON SECOND COM RADIO IS 130.55 AND THERE WAS NO RESPONSE WHEN I ASKED FOR 'ANY SBOUND TFC ON UA315 S OF ALBOG PLEASE RESPOND.' (NOTE: WE ULTIMATELY DSNDED APPROX 600-700 FT TO 38300 FT.) I HAVE BEEN FLYING THIS AIRSPACE FOR OVER 5 YRS NOW AND WITH THE HORRENDOUS ATC (AND/OR UNSCRUPULOUS LATIN AMERICAN OPERATORS FLYING ANY ALTS THEY WANT) THERE WILL BE A MIDAIR COLLISION BEFORE TOO LONG WITH THE 'OPEN SKIES' SO TO SPEAK. WE NEED; AND THE TRAVELING PUBLIC SHOULD DEMAND; SATCOM AND BETTER ATC THAN THIS ARCHAIC LATIN AMERICAN SYS; NOTE ALL THE IATA AIRWAYS ON MAPS WHERE 'ATC IS OF DUBIOUS QUALITY' SO WE ARE TO CALL OUT TO OTHER ACFT ON 126.95 WHEN WE CROSS FIXES AND/OR CHANGE ALTS. THIS AT CLOSING VELOCITIES IN EXCESS OF 900 KTS. ACR X FLT WITH A CREW OF 13 AND 127 PAX DAMN NEAR CRASHED IN THE AMAZON LAST NIGHT! PLEASE DO ALL YOU AND YOUR ORGANIZATION CAN TO 1) GET ATC STANDARDS UP WORLDWIDE OR; 2) GET US OUT OF THOSE AIRSPACES! CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES THIS IS THE SCARIEST EXPERIENCE HE HAS HAD IN 25 YRS OF FLYING. IN SPEAKING WITH HIS UNION SAFETY OFFICER HE LEARNED THAT ANOTHER CARRIER REFUSED TO GO THROUGH MAIQUETIA AIRSPACE FOR SOME TIME BECAUSE OF THE POOR CTL PROCS. PART OF THE PROB IS THAT THERE IS NO RADAR IN THIS AREA AND COM IS ON HIGH FREQ. THEY CAN AND DO GO 100 MI WITH NO COM. THEY HAVE GONE AS LONG AS 45 MINS WITH NO COM. THERE IS NO WAY TO CONFIRM THIS BUT IN CONVERSATIONS WITH OTHER PLTS THERE IS AN AWARENESS THAT THE LATIN/SOUTH AMERICAN PLTS CHANGE ALT WITHOUT CLRNC FROM ATC IF THEY NEED TO FOR SMOOTHER RIDE. THIS OF COURSE LEAVES OTHER PLTS IN THE DARK AS FAR AS POS AND ALT OF OTHER TFC. ALONG WITH THIS IS THE LANGUAGE DIFFICULTY WHEN CTLRS USE SPANISH TO SPEAK WITH SOME PLTS AND RATHER POOR ENGLISH WITH OTHERS. IN THIS SIT; IT WAS NIGHT AND THERE WAS HIGH CIRRUS WHICH CREATED POOR VISIBILITY. HAD THEY NOT HAD TCASII THERE WOULD PROBABLY HAVE BEEN A COLLISION. RPTR FEELS THAT THERE SHOULD BE A COMMON FREQ SUCH AS 130.55 ON WHICH PLTS COULD COMMUNICATE WITH EACH OTHER. HIS OTHER SUGGESTION IS TO FLY 1 MI TO THE R OF THE AIRWAY TO REMAIN CLR OF HEAD-ON TFC. SINCE TFC IN THIS AREA HAS INCREASED BY 400% IN THE LAST FEW YRS SOME ACTION IS NECESSARY BEFORE THERE IS A MIDAIR.