A B737 FLT CREW GOING INTO MKJS HAVE TROUBLE CONTACTING APCH CTLR AND TWR. EVENTUALLY THE FLT CREW DSND ON THEIR OWN IN VFR CONDITIONS AND THEN ARE ABLE TO CONTACT TWR.

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AFTER RESUMING FLTS TO MBJ; AFTER HURRICANE IVAN; I CALLED OUR DISPATCHER FOR A FULL BRIEFING OF ANY ABNORMAL OPS. HE MENTIONED ONLY THAT THEY WERE USING 15 MINS IN-TRAIL ON DEPARTING ACFT. 10 MINS PRIOR TO THE FIR BOUNDARY WE ATTEMPTED CONTACT WITH KINGSTON CTR. WE WERE HANDED OFF FROM HAVANA CTR AT THE BOUNDARY AND CONTINUED TO ATTEMPT CONTACT ON SEVERAL FREQS. THERE WERE SEVERAL OTHER FLTS TRYING TO CONTACT THEM. WE ATTEMPTED TO ESTABLISH A RELAY. WE EVEN TRIED CONTACTING SANGSTER APCH. AT ABOUT 60 NM OUT IN VMC AND WITH THE ISLAND IN SIGHT WE STARTED OUR DSCNT. WE THEN COULD HEAR BITS OF KINGSTON'S XMISSIONS; AFTER WE XMITTED IN THE BLIND. WE HEARD; 'WHO AUTH YOU TO LEAVE FL270?' I RESPONDED; 'CAPT'S AUTH.' ANOTHER ACFT; ACR Y; RELAYED TO CONTACT SANGSTER TWR. WE LEVELED AT FL230 AND ON INITIAL CONTACT WITH SANGSTER APCH ON TWR FREQ; WE WERE CLRED; 'DSND TO LOWEST AUTH ALT AND CLRED FOR THE OMAXI ARR AND THE ILS RWY 7 APCH. WE HAD TO IMMEDIATELY LOWER THE GEAR TO GET ENOUGH DRAG TO MAKE THE DSCNT. THE FLT CONTINUED UNEVENTFULLY FROM THAT POINT.