DC10 CREW HAD NMAC WITH AN MD80 IN SKED CLASS A AIRSPACE.

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ENRTE MIA-SKRG; WHILE BTWN INTXNS BUTAL AND MENTO AND DURING INITIAL DSCNT FROM CRUISE ALT OF FL330; WE RECEIVED INSTRUCTION TO DSND TO FL290 AND THERE WAS OPPOSITE TFC CLBING TO FL280. TCASII NOTED TFC 5 MI R OF NOSE; 30 MI; -7000 FT; XING SLOWLY TO L OF NOSE. AS TFC CLOSED AND CLBED; FO ACQUIRED TFC ON RADAR AT 15 MI. TFC CLBED RAPIDLY WHILE CLOSING. AT FL300 DURING OUR DSCNT; FO NOTED TFC WAS ONLY SLIGHTLY MORE THAN 1000 FT BELOW OUR ALT AND CALLED FOR A R TURN. A CALL WAS MADE TO BOGOTA TO ADVISE OF TFC AND THEY RESPONDED TFC WOULD BE AT FL280. AT FL298; FO NOTED THAT RADAR INDICATED CONSTANT CLOSURE AZIMUTH AND THAT TCASII INDICATED TFC WAS STILL CLBING WITH NO RA (TCASII RA). FO CALLED TO INCREASE BANK 'HARD AS POSSIBLE.' FE NOTED PROX OF TARGET ON TCASII AND ZERO ALT DIFFERENCE AND CALLED FOR TURN. CAPT; WHO WAS BY NOW HAND FLYING AND ON INSTS; IN INTERMITTENT IMC; BANKED 45 DEGS. LEVEL AND AT FL295 IN A 45 DEG R BANK; FO SAW THE TFC (ACR Y MD80/DC9) PASS OFF L SIDE LESS THAN 100 FT BELOW AND 200-250 FT BESIDE IN A SLIGHT L BANK AND STILL IN A CLB. ACFT PASSED IN OPPOSITE DIRECTIONS AT FL295. TO AVOID THE ACR Y ACFT; CAPT WAS FORCED TO EXERCISE EXTREME MANEUVERS. ACTION BY FO AND FE TO CALL FOR MEASURES DESPITE LACK OF RA CLRLY AVOIDED WHAT WOULD HAVE BEEN A MIDAIR COLLISION OTHERWISE. PROBS NOTED: 1) FAILURE OF ACR Y TO LEVEL AT FL280 AS DIRECTED. 2) FAILURE OF BOGOTA CTL TO RECOGNIZE DETERIORATING CONFLICT. 3) FAILURE OF TCASII TO GIVE AN RA; DESPITE GOOD GND CHK (TCASII WAS CONFIRMED BEFORE TKOF AND DURING AS WELL AS AFTER INCIDENT TO BE IN THE TA/RA MODE POS). OUR AVOIDANCE MANEUVER TOOK US FROM INITIALLY 20-25 DEG BANK TO A FULL 45 DEG BANK; AIRSPD SLOWED TO 250 KTS PRIOR TO EVENT; AND HELD DURING EVENT.