AT72 CREW HAD A TCASII TA AFTER THE ZMA RADAR CTLR WAS NOT ABLE TO READ THE ACFT RADIO XMISSIONS. THE CREW HEARD ZMA NORMALLY.

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WHILE APCHING NASSAU AT FL190 WE WERE ADVISED BY ZMA TO DSND TO 11000 FT. WE REPLIED '11000 FT' AS WE INITIATED THE DSCNT AND ONLY A FEW MOMENTS LATER DID ATC AGAIN ISSUE CLRNC TO 11000 FT MSL. WE AGAIN GAVE REPLY; BUT APPARENTLY THEY COULD NOT HEAR US. WE COULD HEAR THEM CLRLY AND WERE ISSUED A CLRNC TO STOP AT 15000 FT MSL AND SQUAWK IDENT ON OUR XPONDER; AS WE DID. THE ACFT WAS ALREADY STARTING PAST 15000 FT WHEN THE COMMAND WAS ISSUED; BUT IN NO INSTANCE WERE WE UNDER 14800 FT FOR MORE THAN 3 SECONDS DURING THE RECOVERY TOWARDS 15000 FT. WE WERE ON FREQ 134.20 MHZ AS INDICATED BY PREVIOUS CTLR AND HAD HEARD ALL XMISSIONS ON THAT FREQ WITHOUT PROB THROUGHOUT THE FLT FROM MCO TO MYNN (NASSAU). IT WAS ONLY AFTER THE PROB WE ENCOUNTERED IN COMMUNICATING WITH THIS CTLR THAT WE ATTEMPTED CONTACT ON A PRIOR FREQ OF 125.70 MHZ WITH VHF #2 AND THAT PROVED SUCCESSFUL. WE ALSO ATTEMPTED TO CONTACT THE PROB CTLR ON VHF #2 WITH FREQ 134.20; BUT STILL DID NOT RECEIVE CONFIRMATION OF OUR XMISSIONS ON THAT XMITTER EITHER. WE WERE ABLE TO FINALLY ESTABLISH 2-WAY CONTACT ON FREQ 133.40 MHZ AFTER THE CTLR ON 125.70 MHZ KINDLY ADVISED US TO TRY THAT ONE. THE CTLR ON 133.40 MHZ WAS INDEED THE SAME CTLR WORKING 134.20 MHZ AND IMMEDIATELY TOLD US THAT HE HAD BEEN ATTEMPTING CONTACT WITH US FOR SOME TIME. WE TOLD HIM THAT WE COULD HEAR HIM CLRLY (HENCE OUR LEVELING AT 15000 FT AND SQUAWK REPLY) AND THAT WE WERE ALSO ATTEMPTING CONTACT THE ENTIRE TIME. HE CLRED US TO THE ORIGINAL ALT OF 11000 FT MSL AND AS WE WERE DSNDING WE COULD HEAR A DASH 8 ON CLBOUT FROM NAS. IT WAS APPARENT THAT THE REASON WE WERE HELD AT 15000 FT AFTER THE ORIGINAL CLRNC TO 11000 FT WAS THE LACK OF COM ON THE CTLR'S PART AND THE OUTBOUND ACFT FROM NAS. WHAT THE CTLR ASSUMED WAS THAT WE WERE EITHER NOT RESPONDING PURPOSELY OR RADIOS WERE NOT FUNCTIONING; BOTH OF WHICH WERE NOT THE CASE. THE CTLR LANGUAGE WAS BORDERLINE CHASTISING WHEN I BELIEVE THAT HE SIMPLY NEVER SWITCHED US TO THE APPROPRIATE FREQ OF 133.40 MHZ AT THE CORRECT TIME. THE FLT CONTINUED ON TO NASSAU WITHOUT FURTHER DIFFICULTIES AFTER WE WERE HANDED OFF TO NASSAU APCH CTL (ALBEIT AT TOO HIGH AN ALT DUE TO THIS SIT) AND LANDED UNEVENTFULLY. I STRONGLY BELIEVE THAT THE CTLR WAS AT FAULT IN NOT ALERTING US TO A FREQ CHANGE EARLIER DURING THE FLT AND THAT HAD WE NOT HEARD HIM CLRLY ON THE FREQ OR ATTEMPTED TO ESTABLISH CONTACT USING VHF #2 WITH THE PREVIOUS CTLR; THE SIT COULD HAVE BEEN VERY SERIOUS. THE CTLR'S ATTEMPT TO BLAME OUR EQUIP OR IMPLY THAT WE WERE NOT LISTENING I FEEL WAS AN IMPROPER ATTEMPT TO COVER HIS OWN MISTAKE.