AN ACR MLG OVERSHOT THE ILS AT LAX CONFLICTING WITH ANOTHER ACFT APCHING THE S RWYS. THIS WAS IN VISUAL CONDITIONS AT LAX; LNDG TO THE W.

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CAPT FLYING SADDE 6 ARR TO LAX. ATIS RPTS FOG VICINITY ARPT 4 MI VISIBILITY; 17/17 2504; ALTIMETER 29.90; LNDG RWYS 24R/25L. APCHING SMO AT 7000 FT MSL; APCH CTL ASKS IF WE CAN SEE LAX. WE REPLY ONLY THE APCH ENDS OF RWY 24L/R ARE VISIBLE THROUGH THE FOG WHEREUPON APCH CTL CLRS US FOR THE STADIUM VISUAL APCH TO RWY 24R. TURNING BASE AT SMO 8.4 DME AT 3500 FT MSL; THE COLISEUM AND HARBOR FREEWAY WERE STILL VISIBLE; BUT NOW THE ENTIRE N HALF OF LAX WAS OBSCURED BY FOG. XING THE SMO 084 DEG RADIAL AT 3000 FT AND 170 KTS; THE DOGLEG TO FINAL WAS INITIATED AND APCH CTL ADVISED 'TURN FINAL NOW; DON'T OVERSHOOT' AS A LIGHT COMMUTER ACFT WAS MAKING AN APCH TO THE S SIDE. AN OVERSHOOT DID OCCUR AND; ALTHOUGH THE COMMUTER ACFT WAS NOW IN SIGHT; WE RECEIVED A TCASII RA OF 'DON'T DSND' AND 'CLB' AND INDICATIONS ON THE CRT HE WAS LESS THAN 1 MI AND 200 FT BELOW US. CORRECTING BACK TO CTRLINE ON INSTS; WE FINALLY REGAINED VISUAL WITH RWYS 24L/R DSNDING THROUGH 2000 FT MSL AND CONTINUED APCH TO NORMAL LNDG. WE RPTED THE POOR VISIBILITY CONDITIONS TO THE TWR AND REQUESTED THEY RELAY OUR SUGGESTION TO APCH CTL THAT NO MORE STADIUM VISUAL APCHS BE FLOWN WHILE PATCHY FOG CONDITIONS EXIST; AND WOULD FURTHER SUGGEST THAT WHEN USING THIS PARTICULAR APCH EVEN IN THE BEST OF UNLIMITED VISIBILITY VFR CONDITIONS; APCH CTL SHOULD SLOW LARGE JET ACFT TO THEIR FINAL APCH SPD WHEN TURNING BASE AT THE SMO 8.4 DME WHENEVER PARALLEL S SIDE APCHS ARE BEING FLOWN.