B757 ON VISUAL APCH TO RWY 24R AT LAX OVERSHOOTS TURN TO FINAL AND TRIGGERS A TCASII RA.

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AT APPROX XA00Z; WE WERE IN CONTACT WITH SOCAL APCH CTL. OUR POS WAS ON THE DOWNWIND; NOT YET ABEAM THE LAX ARPT FOR RWY 24R. WE WERE TOLD TO EXPECT A VISUAL APCH WITH AN 8 MI FINAL. AT THAT TIME; WE WERE AT 4000 FT MSL AT 190 KTS. SOCAL APCH ASKED US TO CALL THE ARPT IN SIGHT. WE DID. THEY GAVE US A 160 DEG HDG FOLLOWED BY A VISUAL APCH CLRNC FOR RWY 24R. THE TURN POSITIONED US INSIDE JETSA (WHICH IS 8.2 DME). I ESTIMATE WE WERE APPROX TURNING ON A 6 MI FINAL. AFTER ACKNOWLEDGING THE VISUAL CLRNC; I IMMEDIATELY CALLED FOR THE GEAR DOWN AND THEN FLAPS 25 DEGS TO EXPEDITE OUR DSCNT (WE WERE NOT EXPECTING A TURN INSIDE JETSA). ALTHOUGH VFR; IT WAS SUNNY AND HAZY AND WE HAD THE ARPT IN SIGHT. WE WERE RAPIDLY DSNDING AND BEGINNING TO TURN TO THE RWY 24R FINAL APCH COURSE. IN THE DSNDING TURN; I SAW TFC ON THE TCASII WHICH WAS S OF OUR POS AND IT APPEARED THAT WE WERE GETTING CLOSER TO THE TFC. NEITHER OF US HAD THE TFC IN SIGHT; SO I IMMEDIATELY INCREASED OUR BANK ANGLE TO MANEUVER AWAY FROM THE TFC. THE TFC WAS SHOWING 2400 FT ON OUR TCASII; WHICH WAS THE ALT WE WERE DSNDING THROUGH. AT THE SAME TIME WE WERE IN AN AGGRESSIVE R BANK (APPROX 30-40 DEGS); OUR TCASII ALERT SOUNDED; 'TFC;' IMMEDIATELY FOLLOWED BY A TCASII RA 'CLB;' IMMEDIATELY FOLLOWED BY 'CLR OF CONFLICT.' AT THE SAME TIME THE TCASII WAS SOUNDING THE SECOND 'CLB;' LAX TWR ISSUED US A TFC ALERT AND AN IMMEDIATE R TURN. THE FO TOLD LAX TWR THAT WE WERE RESPONDING TO A TCASII RA. THE TWR THEN CLRED US TO LAND ON RWY 24L. I BELIEVE THAT IN THE CONCERN OF INITIALLY LOSING ALT TO BE STABILIZED BY 500 FT; I DID NOT TURN TO THE FINAL APCH COURSE FOR RWY 24R IN A TIMELY MANNER; AS I DRIFTED S OF THE RWY 24R FINAL APCH COURSE. IN RETROSPECT; WE SHOULD NOT HAVE ACCEPTED THE VISUAL APCH CLRNC TO RWY 24R WITH A TURN INSIDE JETSA.