B737-300 FLC HAS A DIFFICULT TIME WITH THE APCH WHEN THE AUTOPLT FAILS TO TRACK THE LOC COURSE DURING AN IAP ILS APCH PROC INTO DEN.

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ON A DOG LEG L BASE TO INTERCEPT ILS LOC RWY 35L AT DIA; DSNDING OUT OF 13000 TO 10000 FT. AUTOPLT A ENGAGED ON HDG SELECT; VOR LOC ARMED; #1 NAV TUNED IN MANUAL AND IDENTED. IHSI IN THE MAP MODE. APFDS INDICATED CAPTURE ON VOR LOC AND ACFT INITIATED L TURN TO TRACK THE LOC INBOUND. HOWEVER; THE ACFT CONTINUED ITS L TURN TO APPROX HDG OF 320 DEGS. MAP SHOWS W OF COURSE. APCH INQUIRES; RAW DATA VERIFIES; SELECT HDG MODE AND DIAL IN 020 DEGS TO REINTERCEPT. APFDS ARMS IN THE APCH MODE (NOW CLRED ILS RWY 35L APCH). APFDS INDICATES CAPTURE BUT ACFT IS NOT RESPONDING CORRECTLY -- DISCONNECT AUTOPLT AND ATTEMPT TRANSITION TO RAW DATA. BY THIS TIME WE ARE HIGH AND I AM CONFUSED AS TO WHAT IS GOING ON. APCH QUERIES US ON OUR ABILITY TO COMPLETE THE APCH. WE RESPOND THAT WE SHOULD BE ABLE TO RECAPTURE AND COMPLETE THE APCH. AT THIS TIME I AM HAND FLYING AND WE ARE STILL W OF COURSE. GND CONTACT IN COMING INTO VIEW AND WE SEE THE TERMINAL; WE ARE LINED UP ON THE TWR BTWN RWY 34 AND RWY 35L. WE GET CLRNC TO LAND ON RWY 34. I HAVE HAD APPROX 3 YRS EXPERIENCE ON EFIS B757 EQUIP. I HAVE NEVER EXPERIENCED ANYTHING LIKE THIS AND HAVEN'T A CLUE WHAT HAPPENED. IF IT WAS AN ERROR ON MY PART; I DON'T KNOW WHAT. THIS IS MY THIRD OR FOURTH IN THIS ACFT. MY LAST TIME TO FLY EFIS (1500 TOTAL HRS IN B757) WAS 1992. WE CURRENTLY FLY 5 B737 BASIC ACFT; 2 B737 ADVANCED; 2 B737-300 HARD BALL; AND 1 B737-300 EFIS ACFT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE CAUSE OF THE INCIDENT ISN'T KNOWN. MAINT HAS NOT GIVEN THE RPTR ANY INFO RELATIVE TO THE NATURE OF THE FAILURE TO CAPTURE THE ILS COURSE. THE PIC SAID THAT HE HAD INITIALLY OVERSHOT THE ILS COURSE ON THE INITIAL VECTOR BUT WAS UNDER THE GS. ATC THEN HELD HIM TO AN ALT THAT TOOK THE ACFT THROUGH THE GS. THE ACFT AT THAT POINT WENT TO A 320 DEG HDG; PASSING THROUGH THE LOC COURSE. RPTR ALSO SAID THAT HE HAS HAD 1 OTHER EVENT OF A PARALLEL NATURE WHERE HE WAS HIGH AND FAST. THE SOFTWARE SYS IN THE ADVANCED B737-300 SEEMS TO 'LOSE ITS LOCK' ON THE ILS WHEN THIS SCENARIO IS PRESENTED TO IT. RPTR ALSO ADDED THAT IN THE RPTED EVENT; THAT HIS ILS COURSE INDICATOR WENT FROM R DEV TO A FULL L DEV. THE FO'S DID NOT. SEEMED TO BE A DISCONTINUITY BTWN THE #1 AND #2 ILS COURSE SENSING.