B737-800 CREW FLEW THE ILS APCH TO RWY 26R AT ATL. THE ACFT OVERSHOT THE LOC COURSE; AND THEN PARALLELED THE COURSE.

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AT 5000 FT ON BASE LEG HEADING 180 DEGS; SETTING UP FOR APCH TO RWY 26R ATL; APCH CTL GAVE US A VECTOR TO INTERCEPT THE LOC (240 DEGS) AND TO CALL THE ARPT IN SIGHT. WE CAPTURED THE LOC AT APPROX THE SAME TIME WE RPTED THE RWY IN SIGHT. THE FLT MODE ANNUNCIATOR INDICATED LOC CAPTURE AND GS CAPTURE; THE RAW DATA DISPLAYS WERE CTRED; AS WERE THE FLT DIRECTOR BARS AND THE GUIDANCE CUE IN THE HEADS UP DISPLAY. AS I FLEW THE APCH USING THE HUD; I BECAME CONCERNED THAT THE AIRPLANE LNDG IN FRONT OF US WAS NOT IN SIGHT; AND SHOULD HAVE BEEN PLAINLY VISIBLE. WE THEN REALIZED; AT THE SAME TIME AS THE TWR; THAT WE WERE LINED UP AND FOCUSED ON RWY 26L. AN EASY SIDESTEP AND UNEVENTFUL LNDG WERE ACCOMPLISHED ON RWY 26R AS CLRED. AS WE RPTED THE INCIDENT TO THE TWR ON THE GND; ANOTHER ACFT WHO WAS UNIDENTED RPTED THAT 'THE SAME THING JUST HAPPENED TO US.' A LOGBOOK ENTRY WAS MADE; BUT MAINT FOUND NO SYS FAULTS. FOR CLARIFICATION: THE CORRECT APCH TO RWY 26R WAS SELECTED IN THE FMS DATABASE. BOTH RECEIVERS WERE SELECTED TO THE CORRECT FREQ AND COURSE THE CORRECT IDENT (IGX2) WAS DISPLAYED ON BOTH NAV DISPLAYS. THE FLT MODE ANNUNCIATOR DISPLAYED VOR/LOC (LOC CAPTURE). THE RAW DATA COURSE AND FLT DIRECTOR COMMAND BARS INDICATED ON COURSE. THE GUIDANCE DOT IN THE HUD INDICATED ON COURSE. (I SUSPECT THE PROB WAS RELATED TO THE AIRFIELD EQUIP) OR AN UNLIKELY SEQUENCE OF ERRORS IN CREW COORD; IE; FOLLOWED HEADING COMMAND VICE THE LOC. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE CAPT RECOUNTS THAT THE MOST LIKELY PROB WAS THE VERY HIGH WORKLOAD AT LOC INTERCEPT; GEAR DOWN; CLRED FOR APCH; CHANGE TO THE TWR; FINAL CHKLIST; ALL SLIGHTLY DELAYED ARMING THE FLT GUIDANCE FOR LOC CAPTURE. AS THE LOC WAS ARMED; THE FO TURNED THE HEADING BUG TO RWY HEADING; CAUSING THE FLT GUIDANCE TO REVERT TO HEADING. THE DELAY IN ARMING FOR LOC CAPTURE CAUSED A SLIGHT OVERSHOOT; AND THEN THE FLT GUIDANCE REVERTED TO HEADING; CAUSING THE ACFT TO PARALLEL THE LOC COURSE. THE CAPT CONTACTED THE ACR FLEET MGR TO DISCUSS WHAT HAPPENED. HE SAID THIS HAS HAPPENED BEFORE. THE ACR ATC COORDINATOR CONTACTED THE TWR SUPVR. THE SUPVR SAID THAT NO OTHER ACFT HAD HAD PROBS THAT DAY. SUPPLEMENTAL INFO FROM ACN 584414: WE INTERCEPTED THE LOC AND ROLLED OUT ON STRAIGHT-IN FINAL. BOTH FMS'S CONFIRMED ILS RWY 26R WAS SELECTED. APPROPRIATE RWY 26R FIXES WERE DISPLAYED ON MAP. ILS RWY 26R WAS TUNED AND IDENTED ON BOTH SIDES. IDENT 'IGX2' WAS CONFIRMED ON BOTH DISPLAYS. LOC AND GS WERE CONFIRMED CAPTURED ON BOTH SIDES AND IN THE HUD. WE WERE CLRED FOR THE VISUAL APCH BUT KEPT FLYING REFING THE FLT DIRECTORS AND HUD FOR THE RWY 26R ILS AS A BACKUP. I WAS WATCHING THE PRECEDING TFC ON THE TCASII MAP AND NOTICED THAT IT WAS ABOUT TO TOUCH DOWN 3 MI AHEAD OF US; BUT I COULDN'T SEE IT VISUALLY OVER THE THRESHOLD. THEN I NOTICED THAT HE WAS TOUCHING DOWN ON RWY 26R AND WE DIDN'T SEE HIM BECAUSE THE FLT DIRECTOR AND LOC WERE LINING US UP FOR RWY 26L. I INFORMED THE CAPT AND HE STARTED A SIDESTEP TO RWY 26R. ABOUT THAT TIME; TWR ASKED US TO CONFIRM WHICH RWY WE WERE PLANNING ON LNDG ON. WE LANDED UNEVENTFULLY ON RWY 26R AND I RPTED THE ANOMALY TO TWR. WE ALSO CONFIRMED THAT THE CORRECT ILS WAS TUNED AND IDENTED. ANOTHER ACFT HEARD OUR RPT TO TWR AND SAID HE'D EXPERIENCED THE SAME PROB (ILS RWY 26R LOC COMMANDING A COURSE INBOUND TO RWY 26L) ON FINAL BEHIND US. MAINT TESTED OUR ACFT AND FOUND NO PROBS. WE CAN'T THINK OF ANYTHING WE DID WRONG AND ARE WONDERING IF THE ILS XMITTERS CAN BE ACCIDENTALLY SWAPPED.