B727 CREW HAD TCASII RA.

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X WAS AT 6000 FT. Y WAS IFR AT 5000 FT NBOUND. I WAS ALSO WORKING A VFR AT 6500 FT. TFC WAS ISSUED TO X ON BOTH ACFT. PLT RESPONDED. LATER; X ADVISED HE WAS DSNDING DUE TO AN RA; AND I INFORMED X THE VFR AT 6500 FT WAS BEHIND HIM. HE INFORMED ME THAT HE MUST RESPOND TO THE RA. I AGAIN ISSUED TFC TO HIM AT 5000 FT. X WAS AT 5300 FT WHEN I ISSUED TFC TO Y AT 5000 FT. TCASII WAS RESPONDED TO WHEN PLT KNEW OF BOTH ACFT. X WAS A B727; X AT 6000 FT. Y WAS A PA44; Y AT 5000 FT. THE Z VFR WAS A C421; Z AT 6500 FT. SUPPLEMENTAL INFO FROM ACN 442181: LOCATION: 25 NM FINAL FOR RWY 9L AT FLL. WHILE ON EXTENDED FINAL FOR RWY 9L AT 6000 FT; MIA APCH ADVISED US OF VFR TFC AT 6500 FT. SHORTLY THEREAFTER; THE TCASII GAVE AN RA FOR TFC 400 FT ABOVE US. WE WERE UNABLE TO SEE THE TFC DUE TO THE CLOUDS AT OUR ALT; SO I DSNDED TO 5400 FT IN RESPONSE TO THE RA. AS I BEGAN THE DSCNT; MIA INFORMED US OF IFR TFC AT 5000 FT; SO I CLBED BACK TO 6000 FT SINCE THE TCASII RA WAS OVER. I SPOKE WITH MIA TRACON AFTER LNDG AND EXPLAINED TO HIM THAT WE WERE UNABLE TO SEE EITHER OF THE OTHER ACFT IN OUR VICINITY DUE TO CLOUDS AT OUR ALT. AFTER OUR DISCUSSION; MIA TRACON INFORMED ME THAT THIS EVENT IS CLOSED AND NO ACTION IS CONTEMPLATED BY MIA ATC.