GII FLT CREW REPORTS TCAS RA AND NMAC WITH C337 DURING VISUAL APPROACH TO BHM RWY 24 AT 2800 FEET.

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LETTING DOWN INTO BIRMINGHAM FOR IN-TRAIL APCH BEHIND A B737. MADE POSITIVE VISUAL CONTACT WITH B737 AND APCH CLRED (US) FOR A VISUAL APCH '#2 TO FOLLOW THE B737 ON FINAL.' AT THIS TIME A C337 WAS VFR AND WAS ASKED IF HE HAD A POSITIVE VISUAL CONTACT ON THE G2 ON FINAL; AS IT WAS HIS TFC TO FOLLOW! HE REPLIED 'GULFSTREAM IN SIGHT.' WE DSNDED OUT OF 4000 FT AND STARTED A TURN (THROUGH 330) TO INTERCEPT THE INBOUND COURSE (236) AND PASSING 3000-2800 FT WE RECEIVED AN RA AND IMMEDIATE CLB. WE COMPLIED! MOMENTS LATER ONE OF OUR PAX CAME FORWARD AND ASKED IF WE SAW THAT 'AIRPLANE THAT JUST WENT REAL CLOSE TO OUR TAIL AND BELLY?' WE ASKED HIM TO RETURN TO THE CABIN AND REASSURED HIM HE WAS SAFE! MY CO-CAPT NOTED THE 'RED' RA SHOWED 100 FT AS I BEGAN TO PULL UP! AFTER WHICH THE CTLR REPLIES; 'TURN L HDG 330 AND INTERCEPT LOC.' MY CO-CAPT STATED; 'WE CLRED FOR VISUAL APCH' AND THE CTLR PAUSED AND AGREED! THE C337 AFTER LNDG MADE A COMMENT TO THE GND CTLR AFTER HE LANDED 'DON'T SEEM TO HAVE ENOUGH CTLRS OUT THERE; HAVEN'T FLOWN A SKYMASTER LIKE THAT SINCE CAMBODIA; HA; HA; HA!' 1) FIRST I BELIEVE BIRMINGHAM FINAL IS TOO MECHANICAL. WE HAVE RECENTLY BEEN PLACED OUTSIDE OF THE MARKER (8-10 MI) IT APPEARS TO PLACE AIRLINE TFC IN PRIORITY. BY THE SAME HANDLING WE END UP AT 170 KTS OR LESS (VERY SLOW FOR A LARGE JET) AND FORCED TO FOLLOW C172'S AND THE LIKE TO ACCOMMODATE THE 'CTLRS.' WE ASKED TO BE CLRED TO RWY 36 (OUR SHORTER NS RWY) AND WERE DENIED AND FELL INTO LINE SOMEWHERE BTWN 7 AND 8 IN LINE. OUR PREVIOUS CTLRS SEEMED TO UNDERSTAND 'HOW TO MANEUVER JET TFC IN BETWEEN (SPD DIFFERENCES IN APCH VERSUS ON FINAL) SINGLE ENG/LIGHT GA TFC.' NOW IT APPEARS THAT WE ARE 'ALL' VECTORED AS LIKE ACFT. 2) NEXT 'AND MOST IMPORTANT' I DON'T BELIEVE THE CESSNA EVER HAD VISUAL ON US! HE MAY WELL HAVE SEEN THE B737 WE WERE TO FOLLOW AND MISTAKEN IT FOR US; BUT BY HIS COMMENTS AND OUR PAX'S DESCRIPTION OF HIS 'MANEUVER' HE SAW US AT THE LAST MOMENT. AND THE CTLR HAD TO SEE 'IT' COMING! THE VERY NEXT STATEMENT OUT OF THE CTLR WAS 'TURN L TO 330...' HE WASN'T EVEN SURE 'IF HE WAS STILL CTLING US OR THE CESSNA.'