B767 FLT CREW EXPERIENCED CLOSE CALL WITH ANOTHER ACFT AT FL330 UNDER PORTO VELHO CTL IN BRAZIL.

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ON FLT ABC 3 MILES N OF SPRIN INTXN IN CONTACT WITH PORTO VELHO CTL WE EXPERIENCED A SUBSEQUENT TCAS TA/RA IN IFR CONDITIONS AND MANEUVERED TO AVOID IMPACT WITH OTHER ACFT. WE WERE AT 330 IN CRUISE FLT ON THE AIRWAY. ON COMING TFC WAS DISPLAYED ON THE TCAS 1000 FT BELOW OUR ACFT. I NOTED TO THE RELIEF PLT WHO WAS IN THE L SEAT FLYING THAT THE ON COMING ACFT WAS ONLY 1000 FT BELOW US. AS THE ON COMING ACFT PASSED THE 10 MI BAND HE BEGAN TO CLB INTO OUR AIRSPACE. I TOLD THE RELIEF PLT TO TURN R OFF THE AIRWAY TO AVOID; WHICH HE DID. THE ON COMING ACFT CONTINUED TO CLB TOWARD US AND WE RECEIVED A 'TFC; TFC' ALERT. IT SEEMED AS IF THE ON COMING ACFT HAD ALSO TURNED TOWARD US AND WAS CONTINUING HIS CLB NOW AT 400 FT BELOW US. WE ALSO WERE CLBING TO AVOID CONFLICT. THE RELIEF PLT TURNED L TO AVOID WHEN WE GOT THE FULL TA/RA. AT THAT POINT WE BOTH GRABBED THE YOKE AND DISCONNECTED AUTOPLT AND AUTOTHROTTLES. WE TURNED HARDER AND PULLED UP HARDER TO AVOID IMPACT. THE TCAS DISPLAYED ON COMING ACFT WITHIN 100 FT AND CLOSING. WHILE PASSING FL360 WE BROKE OUT OF THE CLOUDS IN A L BANK. THE RELIEF PLT FIRST SAW THE LIGHTS AND WHEN I LOOKED OUT THE WINDOW I SAW AN AIRLINER IN A SLIGHT L BANK PASSING MY RIGHT WINDOW. I COULD SEE FIGURES IN THE WINDOWS. ONCE WE WERE CLEAR OF CONFLICT I CALLED PORTO VELHO CTL AND TOLD HIM WHAT HAD JUST OCCURRED. HE JUST REPLIED MAINTAIN 330 AND ACTED AS IF HE COULDN'T UNDERSTAND WHAT I WAS TELLING HIM. I TOLD HIM I WOULD BE WRITING UP THE INCIDENT. ANOTHER COMPANY FLT CALLED US ON 123.45 TO SEE IF WE WERE OK SINCE THEY HAD HEARD IT ALL ON THE RADIO. I WAS UNABLE TO FIND OUT WHO THE ONCOMING ACFT WAS THOUGH I ASKED NUMEROUS TIMES. PORTO VELHO NEVER ACKNOWLEDGED ANYTHING THEY JUST HAD ME SWITCH FREQUENCIES. NO ONE IN THE BACK OF THE ACFT HAD ANY IDEA WHAT HAD HAPPENED OTHER THAN WE WERE CLBING. WE RETURNED TO 330 AND DEBRIEFED THE CAPT WHEN HE RETURNED FROM HIS BREAK.