AN NMAC IS AVOIDED WHEN 2 B727'S MANEUVER AWAY FROM EACH OTHER NW OF PAP; FO. ONE B727 HAD BEEN CLRED THROUGH THE OTHER'S ALT BY A NON RADAR CTLR AT MTEG CTR IN PORT-AU- PRINCE.

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WE WERE PROCEEDING DIRECT TO JOSES INTXN AT FL260; IN VFR CONDITIONS DAYLIGHT. WE WERE GIVEN DIRECT BY SANTO DOMINGO ARTCC. OUR SCHEDULED PAX TRIP WAS FROM AUA-MCO- PIT; WHICH MY CREW HAD DONE MANY TIMES BEFORE. WE WERE FLT PLANNED AT FL350 BUT DUE TO TFC; WERE TOLD BY CURACAO ATC TO MAINTAIN FL260. WE REPEATED OUR REQUEST FOR FL350 TO SANTO DOMINGO BUT AGAIN TOLD TO MAINTAIN ALT. 10 MINS PRIOR TO JOSES INTXN I GAVE RADIO #1 (PORT-AU-PRINCE) TO MY FO; WHO WAS FLYING; SO I COULD CALL ZMA WITH OUR ESTIMATE FOR JOSES. I LEANED BACK FROM PUTTING THE NEW SQUAWK IN THE XPONDER WHEN I NOTICED THE TCASII WITH A YELLOW CIRCLE WITH A -07 NEXT TO IT. AS I WAS ASKING MY CREW IF THEY HAD THE TFC IN SIGHT; THE TCASII WENT OFF 'TFC; TFC' FOLLOWED IMMEDIATELY BY 'DSND; DSND.' THE VOLUME IS VERY WEAK SO I LOOKED AT THE TCASII AND IT SHOWED A 4000 FPM DSCNT COMMAND. I IMMEDIATELY TOOK CTL OF THE AIRPLANE AND BANKED IT HARD TO THE R (IN EXCESS OF 45 DEGS) AND PUSHED THE NOSE OVER. WHILE I WAS DOING THIS MANEUVER; I LOOKED OUT MY SIDE WINDOW (L) AND I SAW A B727 PULLING UP AND BANKING TO THE R. AFTER WE PASSED EACH OTHER I GAVE THE AIRPLANE BACK TO MY FO AND WE CLBED BACK TO FL260. MY FO WAS STILL MONITORING PORT-AU-PRINCE RADIO AND ADVISED THEM OF THE TCASII RESOLUTION. THE B727 JET DID THE SAME. I WAS STILL TALKING WITH MIAMI AND I ADVISED HIM OF THE RESOLUTION AND HE SAID HE SAW A 700 FT DIFFERENCE AND THAT HE WOULD NOTIFY HIS SUPVR AND MARK THE TAPES. EVERYBODY IN THE BACK OF MY PLANE WAS FINE; OTHER THAN SOME FOOD TRAYS ON THE FLOOR. PORT-AU-PRINCE ATC HAD GIVEN THE B727 JET A DSCNT TO FL230 FROM FL270; WHICH IS WHY HE WAS DSNDING. THE JET CARGO B727 HAD TCASII ALSO AND THERE IS NO DOUBT THAT HAD HE NOT DONE HIS PULL-UP WE WOULD BE DEAD. IF THIS SIT WERE AT NIGHT OR IN IFR CONDITIONS; WE MOST CERTAINLY WOULD BE DEAD. ALL CARGO ACFT NEED TCASII. IT IS ANOTHER BACK-UP SYS IN THE ATC SYS. MY CREW OF 6 AND 86 PAX OWE THEIR LIVES TO TCASII. THE VOLUME ON THE TCASII NEEDS TO BE TURNED UP. SINCE PORT-AU-PRINCE IS NON RADAR; THEY NEED TO PLACE MORE QUALIFIED PERSONNEL INTO THESE POS. SUPPLEMENTAL INFO FROM ACN 470072: EVEN THOUGH HE WAS A CARGO JET (B727) HAD TCASII ALSO. WE ARE ALSO A CARGO FLEET BUT WE WERE FLYING PAX; THEREFORE; WE HAD TCASII. TCASII SAVED OUR LIVES AS HAITI APCH CTL DIRECTED BOTH AIRPLANES IN THE SAME RTE IN OPPOSING XING ALTS. THE REST OF OUR CARGO-ONLY AIRPLANES DON'T HAVE TCASII SINCE IT'S NOT REQUIRED BY LAW. IF THE OTHER CARGO OPERATOR HAD HAD NO TCASII WE WOULD HAVE HAD A MIDAIR CRASH. SANTO DOMINGO NOTICED THE INCIDENT AND WE TOLD THEM TO TALK TO HAITI (WE WERE QUICKLY HANDED OVER TO SANTO DOMINGO). WE WERE ABLE TO COMMUNICATE AFTERWARDS WITH THE OTHER AIRPLANE AND THEY FELT THE SAME WAY WE DID.