B747-200 ON ILS APCH TO RWY 24L AT LAX ENCOUNTERS REVERSED LOC DISPLAY PRIOR TO INTERCEPT. MYSTERIOUSLY CORRECTS ITSELF WHEN ON COURSE.

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WE WERE CLRED AFTER SMO FLY HDG 065 DEGS EXPECT RADAR VECTORS RWY 24R. AT ABOUT 10 DME SMO WE WERE SWITCHED TO RWY 24L; TURN R HDG 160 DEGS. APCH THEN GAVE US TURN R HDG 220 DEGS CLRED FOR ILS RWY 24L; ETC. I SET THE HDG BUG THEN SWITCHED NAV MODE FROM HDG TO ILS AND GOT AN INST COMPARATOR WARNING. LOOKING ACROSS; I NOTED THAT THE FO'S NAV WAS STILL ON FREQ 108.5. I TOLD HIM TO RETUNE TO 111.7 FOR RWY 24L. BACK TO MY SIDE; MY CDI WAS NOW SHOWING ALMOST 1.5 DOTS L OF COURSE; AND THE AUTOPLT HAD NOT STARTED THE TURN. THIS SEEMED A LITTLE STRANGE BUT I HAVE OFTEN HAD TO OVERRIDE THE AUTOPLT TO AVOID AN OVERSHOOT DUE TO HIGH SPD CLOSE-IN TURNS TO THESE RWYS. I DISCONNECTED THE AUTOPLT; STARTED CORRECTING; CHKED FOR FLAGS (NONE); XCHKED THE FO'S INSTS (THEY AGREED NOW) AND LOOKED FOR THE ARPT. WE SWITCHED TO TWR. THEY SAID WE WERE WELL R OF COURSE. WE WERE NOW SHOWING ALMOST 2 DOTS L OF COURSE; NO FLAGS. I TURNED L HDG 220 DEGS AND ASKED IF WE WERE GETTING A GOOD IDENT. BOTH FO AND FE SAID YES. WE SPOTTED THE APCH LIGHTS FOR RWY 25L AND I CONTINUED TOWARD THEM; STILL LOOKING FOR THE N COMPLEX. WE GOT VISUAL WITH RWY 24L INSIDE SUTIE. THE CDI WAS AT FULL R DEFLECTION UNTIL WE CROSSED THE RWY EXTENDED CTRLINE TO THE S; AT WHICH TIME THE CDI STARTED INDICATING NORMALLY. THE GS NEEDLE REMAINED FULL UP THROUGHOUT. I ESTABLISHED A NORMAL VISUAL APCH BY 1000 FT AND LANDED NORMALLY. AFTER BLOCK-IN I CALLED THE SUPVR. HE SAID THAT THERE WERE NO EQUIP WARNINGS OR COMPLAINTS FROM OTHER ACFT FROM THAT TIME. ALL HIS SYS APPEARED TO BE NORMAL. IT HAS ALWAYS BOTHERED ME THAT WE OFTEN GET A LAST MIN RWY CHANGE; SOMETIMES SEVERAL; GOING INTO LAX. ANOTHER PERSONAL COMPLAINT IS THAT THE N COMPLEX IS HARD TO FIND (VISUALLY) UNTIL LINED UP AND CLOSE IN. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: NO PROBS WERE DETECTED IN THE AIRBORNE SYS UPON INSPECTION BY MAINT. ALTHOUGH HE DID SPECIFICALLY ASK FOR AND RECEIVED CONFIRMATION OF THE ILS IDENT FROM THE FO AND SO; HE STATED THAT WHEN HE PERSONALLY SELECTED THE FREQ HE INITIALLY HEARD ONLY STATIC. THIS REINFORCED THE CONJECTURE REGARDING AT LEAST A TEMPORARY ANOMALOUS CONDITION FOR THE ILS XMITTER. HE FURTHER REINFORCED THE FACT THAT ALTHOUGH THEY WERE TECHNICALLY VMC THEY WERE UNABLE TO SEE THE RWY FROM THEIR POS OUTSIDE OF THE FAF.