ACR RPTR HAS A CONFLICT WITH ANOTHER ACR OPPOSITE DIRECTION CLBING THROUGH HIS ALT. TCASII RA ALERTED FLC AHEAD OF TIME.

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OUR WDB X WAS CRUISING SBOUND ON UA301 AT FL330. WE WERE ABOUT 30 NM N OF BARRANQUILLA VOR; IN THE CLR; WITH SCATTERED CLOUDS BELOW OUR LEVEL. TCASII CALLED 'TFC;' AND THE CAPT AND I LOOKED AT OUR SCOPES TO SEE ONCOMING TFC 200 FT BELOW AND CLBING. WE LOOKED OUT AND MADE VISUAL CONTACT JUST AS THE TCASII COMMANDED 'CLB; CLB NOW!' THE CAPT TOOK THE PLANE OFF OF AUTOPLT; AND INITIATED A HARD CLB; AS THE VSI COMMANDED A 2000 FPM RATE OF ASCENT. IN THOSE FEW SECONDS; THE ONCOMING PLANE INDICATED AT OUR ALT; WITHIN 5 MI AND CLOSING. TCASII COMMANDED 'STOP CLB; DSND; DSND NOW!' THE CAPT DID; AND I SAW THE PLANE COMING RIGHT AT US. I SAID 'L; I THINK WE SHOULD BRING IT L.' AND THE CAPT AGREED. WE STARTED ABOUT A 20-25 DEG BANK L. CHANGING OUR HDG ABOUT 15-20 DEGS. I WATCHED AS THE TFC PASSED WITHIN 1000 FT TO OUR R. I LOOKED AT THE SCOPE; AND HE WAS AT OUR ALT. I CALLED TO RPT THIS TO BARRANQUILLA CTL; AND HE SAID WE HAD NO TFC. I INSISTED AND HE SPOKE WITH 2 OTHER ACFT IN SPANISH. HE SAID THEY WERE AT FL310 AND FL350. WE THINK ACR HVY Y THAT CLAIMED TO BE AT FL350 IS THE ONE THAT WE MISSED. ON OUR SCOPE; 10 MI BEHIND US; THE PLANE WAS JUST 900 FT ABOVE US STILL IN A CLB EVEN AS WE RECOVERED TO FL330. THOUGH IT'S POSSIBLE BARRANQUILLA CLRED THE ACR Y TO CLB THROUGH OUR ALT BY MISTAKE; AND WE DIDN'T CATCH IT AND TRIED TO COVER HIS ALTDEV. AFTER RECOVERY; WE CHKED WITH THE FLT ATTENDANTS; AND THEY RPTED NO PROBS IN THE CABIN. THE CAPT MANEUVERED AGGRESSIVELY; BUT SMOOTHLY; AND WHILE THE FLT ATTENDANTS KNEW SOMETHING WAS HAPPENING. I DON'T THINK WE DISTURBED ANY OF THE PAX. FROM THE FIRST 'TFC' CALL; TO THE TIME IT PASSED US; WAS ONLY 20-30 SECONDS. IF WE HADN'T HAD TCASII WE PROBABLY WOULDN'T HAVE SEEN HIM IN TIME TO AVOID HIM; SINCE HE WAS IN AND OUT OF THE SCATTERED CLOUDS BELOW OUR NOSE.