WDB ON AN ILS APCH AND MLG ON A VISUAL APCH TO THE SAME RWY HAVE NMAC JUST EAST OF LAX.

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WE WERE CLRED FOR AN ILS APCH TO RWY 24R WITH SIDESTEP TO RWY 24L WHEN ABLE. VIS WAS RPTED AS 6 MI HAZE BUT WAS CONSIDERABLY LESS THAN THAT. WHEN JUST INSIDE ROMAN; APCH CLRED AN ACR B FLT FOR A VISUAL APCH TO RWY 24R. HE HAD RPTED US IN SIGHT. I IMMEDIATELY RPTED WE WERE STILL ON APCH TO RWY 24R AS WE DID NOT HAVE RWY 24L IN SIGHT. WE WERE NEVER TOLD THE LOCATION OF THE ACR B FLT AND DID NOT HAVE HIM IN SIGHT. AT 900' MSL (ABOUT 800' AGL) WE BEGAN TO SEE THE RWY AND STARTED OUR SIDESTEP MANEUVER. AT THIS POINT WE SAW THE MLG PASSING US ON THE RIGHT; LEVEL WITH US AND CONVERGING AT A RANGE OF BTWN 350'-400'. THE F/O WHO WAS FLYING RAPIDLY INCREASED HIS BANK AWAY FROM THE MLG AND WAS ABLE TO CONTINUE THE APCH AND LNDG ALTHOUGH THE APCH FROM THIS POINT ON WAS SOMEWHAT DESTABILIZED DUE TO THE REQUIRED EVASIVE ACTION AND THE DISTR OF SEEING ANOTHER ACFT THAT CLOSE; AND THEN HAVING TO WATCH HIM TO ENSURE SEP. THIS IS THE SECOND TIME THIS EXACT SCENARIO HAS HAPPENED TO ME. THE FIRST TIME WAS OVER A YR AGO IN AN LGT AND THE OTHER ACFT WAS AN MLG BUT THE SITUATION WAS THE SAME. AFTER TALKING TO THE APCH SUPVR I AM CONVINCED THAT THE PROB LIES WITH THE LAX APCH PROC OF CLRING A STRAIGHT-IN TO RWY 24R; THEN CLRING ANOTHER ACFT FOR A VISUAL TO THE SAME RWY AT THE SAME TIME WITH THE EXPECTATION THAT THE STRAIGHT IN ACFT WILL SIDESTEP IN TIME TO ALLOW BOTH ACFT TO LAND ON PARALLEL RWYS AT THE SAME TIME. THE PROB ARISES WHEN THE STRAIGHT IN ACFT IS UNABLE TO SIDESTEP UNTIL CLOSE IN IF AT ALL. NOW YOU HAVE 1 ACFT TRYING TO FLY FORMATION ON ANOTHER; HOPING HE WILL GET OUT OF THE WAY IN TIME; HE IS TRYING TO SNEAK IN CLOSER SO AS TO BE LINED UP. IN THIS LAST CASE I BELIEVE HE WAS ALSO TRYING TO GET AHEAD TO AVOID OUR WAKE TURB. WE ENDED UP HAVING TO RAPIDLY MANEUVER A HEAVY; WIDE BODY ACFT IN MARGINAL VIS AT LOW ALT--NOT A GOOD SITUATION! APCH SAID THEY DO NOT USE THIS PROC WHEN VIS IS LOW--BUT BOTH INSTANCES HAPPENED WHEN VIS WAS WELL BELOW RPTED. LAX IS A UNIQUE AREA--PARTICULARLY IN THE AFTERNOON. RPTED VIS MAY BE ACCURATE WHEN LOOKING DOWN SUN; BUT CONSIDERABLY WORSE WHEN LOOKING INTO THE SUN. I FEEL APCH NEEDS TO GET A BETTER IDEA OF WHAT THE ACTUAL VIS IS--PERHAPS BY QUERYING PLTS ON APCH AND THEN NEVER UTILIZING THIS APCH WHEN ACFT DO NOT HAVE THE RWY IN SIGHT BY ROMAN. OR; PERHAPS SOMETHING COULD BE PUT IN APCH CHARTS. REQUESTING PIREPS AT ROMAN AND DISCONTINUING THIS APCH WHEN CREWS DO NOT HAVE THE RWYS IN SIGHT.