AN ACR B757 FLC HAS THEIR ACFT TURN OFF COURSE DURING AN ILS APCH TO RWY 25L AT LAX. THE FLC RECOGNIZED THE DEV AND CORRECTED. LATER; THE FLC FOUND THAT THERE HAD BEEN A CHANGE IN THE APCH DIRECTION AND ALTHOUGH THE NEW ILS WAS OPERATING; APPARENTLY SO WAS THE OLD XMITTER.

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IN CLOUDS WITH AUTOPLT ENGAGED AND TRACKING RWY 25L LOC IN LNAV. ALL IS WELL; BUT GAATE APCH FIX IS NOT IN FMS; SO FO SELECTS ILS MODE ON EHSI FOR ILS DME. ABOUT 2 NM LATER; ACFT BEGINS A R TURN AWAY FROM LOC (TOWARD OTHER RWYS AND ACFT). AS PF; I SWITCH TO HDG SELECT MODE OF AUTOPLT AND CORRECT BACK. WHILE ON COURSE; MAP SHOWS AN INCREASING TRACK DEV AWAY FROM COURSE. AT FAF (BASED ON DME); THE MAP/FMC SHOWS US DEVIATING 10 DEGS OFF COURSE AND STILL 3 MI TO GO. STOPPED ON GND ON TXWY M BTWN RWYS 25L&R; MAP/FMC SHOWS US 1.3 NM OUT ON FINAL; -3036 FT ON VNAV PATH; AND A GND SPD OF 20 KTS. AT GATE XX; LAST FMS POS IS 3 MINS OFF IN LONGITUDE FROM COMMERCIAL CHART COORDINATES. PER NORMAL OP; FMC FINALLY DROPPED OUT OF NAV MODE AWAITING NEW RTE. ALL OPS NORMAL ON RETURN FLT TO PHX. FOR SOME REASON; THIS ACFT FMS RADIO UPDATED AWAY FROM COURSE AT A CRITICAL POINT IN OUR FLT. THE ONLY 'ALERT' OF THIS MALFUNCTION WAS OUR SITUATIONAL AWARENESS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR WAS FLYING A B757-200 WHEN IT TURNED OFF OF THE ILS COURSE. HE MADE AN ENTRY IN THE MAINT LOG CONCERNING AN FMS ERROR; BUT THE MAINT PERSONNEL WERE UNABLE TO DUPLICATE THE INCIDENT. HIS CHIEF PLT LATER INFORMED HIM; ACCORDING TO THE RPTR; THAT THE LAX CTLRS HAD ADMITTED THAT BOTH THE RWY 25L AND THE RWY 7R ILS XMITTERS WERE OPERATING AT THE SAME TIME AND THEREFORE THE FMS PROBABLY UPDATED BY USING THE DME AND LOC SIGNAL FROM THE NEAREST XMITTER; THAT OF RWY 7R. THE CAPT SAID THAT HIS COMPANY'S STANDARD PRACTICE IS TO HAVE BOTH PLTS SELECT MAP MODE FOR THE APCH. THIS PREVENTS THE FMS FROM UPDATING ITS POS. REQUIRING THE PNF TO TUNE THE ILS FREQ AND TRACK IT IN THE ILS MODE ALLOWS THE FMS TO USE AUTOMATIC TUNING TO VORS IN THE AREA WHILE TRACKING THE ILS'S RAW DATA. THE OTHER NAVAID'S DATA THEN CONTINUOUSLY UPDATES THE FMS'S POS. THE CHIEF PLT; ALLEGEDLY TOLD THE CAPT THAT THE COMPANY'S APCH POLICY WAS UNDER REVIEW.