AFTER RPTING A DC9 IN SIGHT INBOUND TO LAX RWY 25L; PLT IN LTT ACR ACCEPTS A TURN TO 340 DEGS AND A CLRNC FOR A VISUAL APCH TO RWY 25R.

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WHILE BEING VECTORED FOR APCH TO RWY 25L AT LAX; APCH TOLD US TO EXPECT RWY 25R. WE WERE S OF THE AIRFIELD WHICH MEANT WE WOULD HAVE TO CROSS RWY 25L LOC AND FINAL APCH COURSE. WHILE HDG 110 DEGS AND AT 5000 FT; APCH DSNDED US TO 4000 FT. THEY THEN GAVE US TFC AT 9 O'CLOCK POS AND APPROX 4 MI; A HVY B757. WE ACKNOWLEDGED THE B757 IN SIGHT. HE THEN GAVE US ACR Y; A DC9; AT 11 O'CLOCK POS AND 4000 FT. WE ACKNOWLEDGED THIS AND CALLED THIS TFC IN SIGHT. APCH CTL TOLD US THE DC9 WAS FOR RWY 25L; WE WERE FOR RWY 25R. 'TURN L HDG 340 DEGS AND GO BEHIND THE DC9; CLRED FOR VISUAL APCH RWY 25R.' IMMEDIATELY AFTER TURNING TO 340 DEGS IT WAS APPARENT WE WERE ON A COLLISION COURSE WITH THE DC9. OUR TCASII CONFIRMED IT. WE IMMEDIATELY CLBED TO 4500 FT AND WATCHED THE DC9 PASS DIRECTLY BENEATH US! WE JOINED THE RWY 25R FINAL APCH COURSE ABEAM THE DC9 ON RWY 25L AND MADE A NORMAL LNDG. AFTER LNDG; GND CTL TOLD US 'ACR X; APCH SAYS THANKS.' THIS IS TYPICAL AT LAX. TOO MANY AIRPLANES; TOO LITTLE AIRSPACE. MY KINGDOM FOR 5 MI IN TRAIL SEPARATION!