HDG TRACK POS DEV IN A GROSS NAV ERROR DURING APCH PROC STAR.

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CLRED FOR THE CIVET. CIVET 3 PROFILE DSCNT INTO LAX I STARTED TO FLIP MY VOR FROM AUTO-TUNE TO ILS/DME FREQ 109.9 ILAX AND BACK TO AUTO-TUNE AT ABOUT 160 NM FROM LAX ACCORDING TO THE FMS. THE FIRST TIME I SWITCHED; THE DME SHOWED ABOUT 110 IN THE OVERRIDE MODE AND SINCE WE WERE 160 OUT ACCORDING TO THE FMS/RNAV I ASSUMED THE DME WAS FROM SOME OTHER 109.9. I FLIPPED BACK AND FORTH SEVERAL MORE TIMES IN THE NEXT FEW MINS AND BECAME VERY CONCERNED WHEN THE DME FINALLY SHOWED 56 AND THE FMS/RNAV SAID 106; SINCE I KNEW THERE COULD BE NO OTHER ILS/DME WITHIN 100 OF LAX ON FREQ 109.9. AT THAT POINT; I TOLD THE CAPT THERE WAS SOMETHING SCREWY GOING ON WITH MY DME VERSUS RNAV. WE STARTED TO COMPARE HIS VOR TO MINE AND THE RNAV; BUT WITHIN 30 SECONDS; CTR CALLED TO CONFIRM OUR CLRNC ON THE CIVET 3 PROFILE. WE AGREED WE HAD BEEN CLRED FOR IT AND HE REPLIED WE WERE S OF COURSE; GAVE US A VECTOR TO INTERCEPT THE LOC AND ASSIGNED A XING ALT AT ARNES. SINCE WE WERE AT 49 DME WHEN THE CONVERSATION STARTED; WE WERE ALREADY INSIDE CIVET AND LATER ESTIMATED WE MUST HAVE BEEN AT LEAST 1500 FT HIGH XING ABEAM IT. WE WERE BACK ON THE PROFILE BY ARNES. WE DON'T KNOW WHERE OR WHEN THE RNAV GOT LOST; BUT WE DO KNOW THE WAYPOINT COORDINATES WERE CORRECT. THE BOTTOM LINE IS THE OVERALL SYS WORKED. WHILE WE TRUSTED THE RNAV; WE DID START TO XCHK IT; THEN QUESTION IT; AND THE MOMENT THE CTLR CONFIRMED OUR SUSPICIONS; CORRECTED IT BY SWITCHING BACK TO THE OLD- FASHIONED; MANUAL METHOD. SUPPLEMENTAL INFO FROM ACN 219990: I ESTIMATE WE WERE 2-3 MI S WHEN CALLED. EVIDENTLY OUR AUTO NAV SYS HAD MALFUNCTIONED ALTHOUGH WE HAD NO FLAGS. AFTER LNDG WE CHKED OUR INS COORDINATES AND BOTH INS WERE CORRECT. WE SUSPECTED PROBLEM IN RNAV SYS AND ADVISED MAINT TO CHK IT OUT. ONE METHOD OF PREVENTION OR CORRECTION WOULD BE TO XCHK MANUAL SYS A BIT FARTHER AWAY AND MAYBE XCHK MORE THAN ONCE. IN MY 4 YRS AND OVER 2800 HRS USING INS NAV; I'VE ALWAYS FOUND THE SYS TO BE VERY ACCURATE UNTIL THIS INSTANCE.