ACR X TCASII RA HAD NMAC WITH FOREIGN ACR Y NON ADHERENCE TO ATC CLRNC. EVASIVE ACTION TAKEN.

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ACR X FLYING THE ILS APCH IN VMC TO LAX RWY 25L. SOMEWHERE AROUND 15 MI OUT FROM LAX; APCH CTL POINTED OUT TO US ACR Y AT 2 O'CLOCK WHICH WAS ON A R BASE LEG FOR 24R. ACR Y WAS CLRLY VISIBLE AS WE CONTINUED ON OUR ILS AND WE ANTICIPATED ACR Y MAKING HIS R TURN TO FINAL. HE DID NOT MAKE HIS TURN TO FINAL. OUR ACFT AND ACR Y WERE ON A NEARLY PERFECT COLLISION COURSE; BUT WE WEREN'T OVERLY CONCERNED SINCE HE WAS SUPPOSED TO TURN R AND FLY PARALLEL TO US. NOT MUCH TIME WAS AVAILABLE TO US FROM THE TIME WE COULD DETERMINE THAT ACR Y WAS NOT GOING TO TURN AND THE TIME FOR US TO GET OUT OF HIS WAY. AT ABOUT THE TIME THAT WE WERE GOING TO CLB TO AVOID THE TFC; THE TCASII RESPONDED WITH A TA AND VERY SHORTLY WITH AN RA. WE CLBED FROM AN ESTIMATED 3300 FT TO 3900 FT AS ACR Y WENT DIRECTLY UNDER US. AFTER THE CLB ACR Y WAS AGAIN VISIBLE AT ABOUT 8 O'CLOCK AND WAS IN A R TURN. WE STAYED AT OUR NEW ALT AS ACR Y CONTINUED HIS R TURN AND THEN PASSED BELOW US AND BEHIND. APCH CTL ADVISED US WHEN HE WAS CLR OF US BACK ON OUR R SIDE AND CONTINUED OUR APCH VISUALLY TO RWY 25L. OBSERVATIONS AND THOUGHTS -- APCH CTL ADVISED US SEVERAL TIMES OF ACR Y'S POS AND THEY TOLD US TO MAINTAIN SOME ALT (CAN'T REMEMBER WHAT ALT) WHEN THEY REALIZED THAT ACR Y WASN'T TURNING TO FINAL. I HAD DECIDED TO CLB AS THE BEST EVASIVE RTE BECAUSE WE WERE IN LGT AND OUR WT WAS RELATIVELY LIGHT AND I WAS SURE WE COULD OUT PERFORM WDB UNDER THIS SIT. ALSO; I FIGURED THAT SOME CONFUSION OR OVERLOADING OF DUTIES WAS PROBABLY OCCURRING IN THE WDB COCKPIT. SUPPLEMENTAL INFO FROM ACN 244099: I TOLD CAPT; WHO WAS FLYING; THAT THERE WAS A CONFLICT; HE STOPPED DSCNT AT APPROX 3300 MSL AND CLBED TO APPROX 3800 FT. WE DID GET AN RA ON TCASII; HOWEVER; WE HAD ACR Y VISUALLY AND DID NOT NEED TCASII INPUT. CTLR WAS NOTIFIED OF CONFLICT; WE WERE INSTRUCTED TO DSND BACK TO 3500 FT AND THEN SOON AFTER CLRNC TO COMPLETE THE APCH TO RWY 25L.