AN ACR WDB FLC FINDS THAT UPON ARMING THE APCH MODE; AFTER RECEIVING CLRNC APPROX 15 NM OF THE ARPT; THE ACFT TURNED TO A COURSE THAT PARALLELED THE APCH COURSE WITHOUT INTERCEPTING IT. THE FLC WAITED AND THEN ARMED THE APCH MODE WITHIN 1 MI OF THE ILS AND THE ACFT THEN PERFORMED NORMALLY.

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ON HDG 025 DEGS AND 4000 FT W OF ILS RWY 35R AT MXP ALT AND HEADING ASSIGNED BY ATC TO INTERCEPT ILS FOR CAT IIIB APCH. ARMED APCH MODE AND AUTOPLTS APPROX 3-5 MI W OF LOC COURSE AND ACFT EXECUTED IMMEDIATE L TURN PARALLELING APCH. REENGAGED HEADING SELECT AND RETURNED TO INTERCEPT HEADING. VERIFIED AND POSITIVELY IDENTED THAT WE HAD ENTERED PROPER COURSE; APCH AND FREQ. ALL CHKED OK. REARMED APCH MODE AND AUTOPLTS AND MANEUVER OCCURRED AGAIN AND ACFT STARTED DOWN (LOST 300 FT). DISCONNECTED AUTOPLT SELECTED HEADING SELECT AND MANUALLY RETURNED TO ALT AND INTERCEPT HEADING. WAITED TILL LESS THAN A MI FROM LOC COURSE AND REARMED APCH MODE AND AUTOPLTS. ACFT THEN EXECUTED NORMAL CAT IIIB AUTOLAND APCH. WE WERE LESS THAN 15 MI RADIUS FROM ARPT DURING ENTIRE INCIDENT. MAP/LOC/GS INDICATORS NEVER CORROBORATED WE WERE ON APCH IN FIRST 2 INSTANCES. RELATED INCIDENT TO OUTBOUND CAPT AND HE STATED HE'D HAD A SIMILAR EXPERIENCE; BUT NO OTHERS HAVE BEEN RPTED BEFORE OR SINCE. ALSO HEADING BUG SLEWED TO INBOUND COURSE AS IF LOC CAPTURE HAD OCCURRED; EVEN THOUGH LOC/GS NEEDLES WERE OFF SCALE. HAD NO INDICATIONS OF ACFT SYS MALFUNCTION; NOTIFIED MXP STATION MGR; WHO CONTACTED ITALIAN AVIATION AUTHS AND THEY ASSURED US ILS WOULD BE CHKED.