AN ACR DC9-41 FREIGHTER CREW LANDED AT THE WRONG ARPT. ERROR ADMITTED.

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FLT ORIGINATED AT ANC AND HAD A THROUGH STOP AT BIL ENRTE TO A PLANNED TERMINATION AT ILN. THE CAPT CALLED THE COMPANY WHILE I COMMUNICATED WITH CTR. IT BECAME APPARENT THAT WE WERE GOING TO BE REDISPATCHED TO SBN. WHILE THE CAPT TOOK DOWN THE PERTINENT INFO FROM THE COMPANY; I WORKED A NEW CLRNC DIRECT SBN. BY THE TIME WE TURNED THE ACFT TOWARD SBN AND TUNED THE GIJ VOR; WE WERE AT FL330 AND ABOUT 75 DME FROM GIJ. CTR GAVE US A DSCNT IN STEPS DOWN TO 3000 FT AND A VECTOR TO FINAL FOR RWY 27L AT SBN. (WE WERE EXPECTING RWY 09R SINCE THE WX WE GOT FROM THE COMPANY SAID WINDS WERE 170 KTS AT ABOUT 7 MI.) BY THE TIME THE CAPT GOT DONE WITH TALKING TO THE COMPANY; WE WERE BTWN 14000 FT AND 12000 FT. THE INITIAL VECTOR FROM CTR WAS 315 DEGS; ABOUT 30-40 DME FROM GIJ. THE CAPT RAN THE DSCNT CHKLIST AND BRIEFED THE APCH WHILE WE SEARCHED FOR THE ARPT. WE FINALLY SAW THE N/S AND E/W RWYS AT WHAT WE THOUGHT WAS SBN. WE CALLED THE ARPT IN SIGHT WITH CTR AND WERE CLRED FOR THE VISUAL APCH AND SWITCHED TO CTAF. WE REALIZED WE WERE TOO CLOSE TO THE ARPT AND NOT LINED UP ON FINAL FOR RWY 27; SO WE FLEW NBOUND TILL XING THE EXTENDED RWY CTRLINE AND MADE A R 270 DEG TURN TO FINAL ADVISING TFC ON CTAF. WE ROLLED OUT ON FINAL WITH NO GS AND ERRATIC LOC INFO BUT HAD THE RWY AND VASI'S IN SIGHT. WE MANEUVERED TO ALIGN OURSELVES WITH THE EXTENDED RWY CTRLINE AND STARTED A DSCNT UPON INTERCEPTING THE VASI GS. THE RWY APPEARED TO SCALE WITH THE VASI'S AND WE KNEW THE N/S RWY ALSO EXISTED. SO WE THOUGHT THIS WAS THE CORRECT ARPT. IT WAS NOT UNTIL WE TAXIED CLR OF THE RWY AND THE TXWY DID NOT MATCH OUR ARPT DIAGRAM THAT WE REALIZED WE WERE AT EKM. WE WERE DIVERTED ENRTE TO AN ARPT NEITHER PLT WAS FAMILIAR WITH. BOTH PLTS WERE MISSION ORIENTED AND WANTED TO PICK UP THE FREIGHT AND GET IT TO THE HUB AS EXPEDITIOUSLY AS POSSIBLE. VERY SIMILAR ARPT LAYOUT WHEN FLYING AT NIGHT. BOTH PLTS HAD BEEN IN THE SEAT FOR OVER 6 HRS WITH VERY LITTLE TIME TO REST; EAT; OR EVEN STRETCH AT BIL ENRTE. I PERCEIVED THAT I HAD BEEN VECTORED TO THE ARPT AND NOT TO FINAL APCH. SO WHEN I SAW THE ARPT WHICH 'LOOKED' LIKE THE ARPT I WAS LOOKING FOR; I THINK I SAW THE ARPT I WANTED TO SEE.