ACR X TCASII RA HAD LTSS FROM ACFT ASSIGNED SAME ALT. SYS ERROR. EVASIVE ACTION TAKEN.

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ACR X; A REGULAR SCHEDULED FLT OPERATING MIA-DZE (BUENOS AIRES); OPERATING ABOUT 1 HR LATE BECAUSE OF JOB ACTION OF MAIQUETIA (VENEZUELA) CTL AND BARRANQUILLA (BA) COLUMBIA CTL. TKOF FROM MIA WAS VERY NEAR MAX WT REQUIRING MAX ALT OF FL290. AFTER FUEL BURN; CLBED TO FL330 AT MAX RECOMMENDED WT. AT THE TIME OF INCIDENT; WE WERE STILL NEAR MAX WT FOR ALT (CLB PERFORMANCE LIMITED). COCKPIT LIGHTING WAS REDUCED TO MOSTLY INTEGRAL INST LIGHTS; EXTERIOR LIGHTING WAS BEACONS; STROBES; NAV AND LOGO LIGHTING ON. TCASII WAS ON WITH RANGE SET AT MAX (40 MI); RADAR WAS OFF. FLT ATTENDANT HAD JUST SET CREW MEAL ON MY LAP. TCASII SOUNDED TFC. ALL EXTERIOR LIGHTS WERE IMMEDIATELY TURNED ON. TCASII SOUNDED CLB; CLB; NOW. AUTOPLT WAS DISCONNECTED; CLB INITIATED AND THRUST WAS IMMEDIATELY AND AGGRESSIVELY APPLIED. IVSI SHOWED RED ARC FROM ABOUT 1500 FT UP TO 3000 FT DOWN. TCASII RA STOPPED READING FL340. TFC Y PASSED AND WE DSNDED BACK TO FL330. FO OBSERVED TFC AS IT PASSED OFF R WING AT 1/2 MI OR LESS RANGE. NEAR MISS WAS BROADCAST TO CTL. DURING RA MANEUVER EGT LIMITS WERE EXCEEDED ON ENGS #2; #3; AND 4. N1 LIMIT EXCEEDED ON EGT #2. MAINT WAS REQUIRED AT EZE. EGT INDICATORS HAVE AMBER LIGHTS WHICH COME ON 15 DEGS BELOW LIMIT. WHEN LIGHTS CANE ON; PWR WAS REDUCED. NO PAX OR CABIN CREW WERE INJURED OR ALARMED DURING RA. IN SPITE OF THE HR; I FELT GOOD AND ALERT AFTER TAKING A 4-5 HR NAP PRIOR TO DUTY. CONCLUSION: WE JUST PASSED DAGAN INTXN; THE FLT INFO REGION BTWN BA AND BOGOTA CTL AND WERE CHANGING FREQ FROM BA TO BOGOTA CTL SO WOULD NOT HAVE HEARD TFC'S POS RPT AT EJA. UNKNOWN TFC WAS NBOUND AT WRONG ALT. TFC ALWAYS SEEMS HVY BTWN EJA AND BA. THERE HAVE BEEN TOO MANY NEAR MISSES IN SA AND THE CHANCES ARE NOT GETTING ANY BETTER. (HOW DO YOU CHANGE A CULTURE?) I DON'T KNOW ANY WAY TO CHANGE MY OP TO MAKE IT ANY SAFER. MY NEXT TRIP DOWN HERE WILL BE MY LAST; TRANSFERRING TO DIFFERENT ACFT AND DOMICILE. POS RPTS IN SA ARE MADE IN NATIVE TONGUE AND SOMETIMES NOT UNDERSTOOD.