NMAC BTWN AN A300 IN AN ILS APCH TO RWY 7 AND A CLBING C208 NEAR THE LOC COURSE 2 NM SW OF MKJS; FO.

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WE WERE CLRED BY APCH CTL TO FLY DIRECT OMOXI CLRED FOR THE ILS RWY 7 AT MKJS. WX AT THE FIELD WAS RPTED 10 MI VISIBILITY TO THE E AND LESS; 1-2 MI VISIBILITY TO THE W. WE WERE INSIDE THE OM DSNDING ON THE GS AND ON THE LOC WHEN I NOTICED TFC POP UP ON THE TCASII SLIGHTLY L OF CTRLINE BTWN US AND THE RWY. DSNDING BELOW 1000 FT WE GOT A TA. AT AROUND 700 FT THE TFC WAS SHOWING 300 FT BELOW US AND LESS THAN 1 MI. I TOLD THE CAPT THIS DID NOT LOOK GOOD; I WAS GOING AROUND. AFTER STARTING THE GAR WE RECEIVED AN RA AND THE TFC WAS 200 FT BELOW US SHOWING A CLB. WE EXECUTED THE MISSED APCH IN NAV AND FLEW THE WHOLE MISSED APCH AND CLBED TO THE MISSED APCH ALT OF 3000 FT. ON THE MISSED APCH WE ASKED THE CTLR WHAT WE ALMOST HIT. SHE SAID IT WAS A C208 AND HE WAS NOT WHERE HE WAS SUPPOSED TO HAVE BEEN. WE EXECUTED THE WHOLE MISSED APCH AND WAS CLRED FOR THE SAME APCH AGAIN WITH A SUCCESSFUL LNDG. WHEN ON THE GND I CALLED THE DISPATCHER AND CHIEF PLT. AFTER DISCUSSING WITH THEM I CALLED THE TWR. THEY TOLD ME THE TAIL NUMBER OF THE C208. THEY TOLD ME THAT THEY TALKED TO THE PLT OF THE CESSNA AND HE SAID HE HAD A VISUAL ON US. I TOLD THEM HOW COULD HE IF WE WERE IMC WHEN THE NEAR MISS OCCURRED. THEN THEY TOLD ME THAT HE SAID HIS XPONDER WAS MALFUNCTIONING. HE ALSO TOLD THEM HE WAS 1 1/2 MI N OF THE FINAL APCH COURSE. ON THE SECOND APCH WE DID NOT PICK UP THE RWY UNTIL WE WERE AT 600 FT. DURING THE FIRST APCH WE NEVER SAW THE ARPT OR RWY AND WE WERE IN VERY HVY RAIN AND IMC THE WHOLE TIME. 2 PAX IN FIRST CLASS DID SEE THE ACFT OUT OF THEIR WINDOWS ON THE L SIDE OF THE ACFT. THEY WERE SITTING IN THE 2 FIRST ROWS OF FIRST CLASS WINDOW SEATS. SUPPLEMENTAL INFO FROM ACN 609960: FLT ATTENDANT OVERHEARD A PAX IN FIRST CLASS TELLING ANOTHER HE SAW A SMALL ACFT PASSING VERY CLOSE UNDERNEATH US ON THE L SIDE OF THE ACFT. TWR SAID THEY PULLED THE VOICE TAPES. THERE IS NO DOUBT IN MY MIND THAT THIS WOULD HAVE BEEN A MIDAIR; IF IT WAS NOT FOR TCASII AND THE QUICK ACTION OF MY FO.