NMAC. FLC OF AN MDT DURING A FINAL VISUAL APCH STOPPED DSCNT AND CLBED IN RESPONSE TO A TCASII RA CAUSED BY ANOTHER ACFT IN CLOSE PROX FOR A PARALLEL RWY.

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JUST PRIOR TO HUNDY (12.21 LAX); SOCAL ASKED IF FIELD WAS IN SIGHT; CHANGED LNDG RWY TO 25R AND SLOW SPD TO 180 KTS AND STATED THAT TFC AHEAD WAS 'HVY' ACFT. APCHING 3400 FT AND SLIGHTLY L OF RWY 25R CTRLINE (LOC COURSE); RECEIVED TCASII 'TA' AT 3100 FT. GEAR AND FLAPS WERE EXTENDED AS SPD PERMITTED PRIOR TO 'TA.' COULD NOT XMIT TO SOCAL BECAUSE OF NON STOP DIALOGUE (SOCAL/OTHER ACFT ON APCH BEHIND US). SLOWING DSCNT TO 3200 FT; RECEIVED TCASII 'RA' AT 3000 FT. IMMEDIATE LEVEL OFF/CLB INITIATED TO 3500 FT. 'RA' THEN 'TA' SHORTLY DISAPPEARED. SIMULTANEOUSLY PNF SWITCHED TO TWR AND RPTED 'RA.' TWR SAID TFC WAS SAAB COMMUTER; AND COMMUTER HAD US IN SIGHT. VISUAL APCH; LNDG AND TAXI-IN WERE UNEVENTFUL. UPON CONTACTING GND CTL WE ASKED FOR SOCAL APCH TELEPHONE NUMBER. APPROX 15 MINS AFTER LNDG; CALLED SOCAL APCH AND SUPVR DID NOT KNOW ABOUT INCIDENT. HE; ALSO; STATED THAT SECTOR SUPVR WAS 'ON BREAK.' I STATED OUR SIT AND TOLD HIM IT WAS AN 'NMAC.' I ALSO SAID A RPT WOULD BE FILED. 3 IMPORTANT ITEMS WERE NOT COMMUNICATED. NO ADVISORY OF 'HVY' ACFT PRECEDING US. NO ADVISORY OF TFC AND SAAB COMMUTER FLYING PARALLEL APCH; OR; THAT COMMUTER HAD US IN SIGHT. NO SWITCH-OVER TO TWR.