FATIGUE CITED AS A REASON FOR A LOC OVERSHOOT AND DEGRADATION OF CREW PERFORMANCE.

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APCHING ATL; WE WERE CLRED ON A HDG TO INTERCEPT RWY 26R LOC. FO WAS PF. I WAS MONITORING ATL VOR FOR DISTANCE AND AZIMUTH INFO. FO WAS ON RWY 26R LOC. HE FLEW THROUGH THE LOC. I CORRECTED HIM AND HE MADE THE ADJUSTMENT TO REINTERCEPT THE RWY 26R LOC BUT NOT BEFORE XING THE APCH COURSES FOR THE S RWY COMPLEX. CONTRIBUTING FACTOR WAS OUR CHARTER CARRIER'S OVERSEAS RULES DO NOT PROVIDE FOR REST. THE ONLY LIMITATION WE ARE SUBJECT TO IS THE 12 HR MAX IN 24 HR. WE SHOWED FOR DUTY IN CHS AT XA30Z ON FEB/THU/02; OPERATED TO ATL; SPENT 3 HRS ON GND AND OPERATED TO EDDF. UPON ARR AT HOTEL; WE HAD 7 HRS UNTIL SHOW-UP FOR NEXT DUTY. ACTUAL TIME SLEEPING FOR FLT DECK CREW WAS BTWN 4-5 HRS. WE THEN OPERATED EDDF/BGR/ATL. WE ALSO HAD A 3 HR GND TIME IN BGR. ENRTE FROM BGR TO ATL WE WERE EXHAUSTED. WE LANDED IN ATL AT XA20Z FEB/SAT/02. THAT'S 5 HRS SLEEP DURING A 40 HR 50 MIN PERIOD. HAD I REALIZED JUST HOW BEAT WE WERE IN BGR I WOULD HAVE CANCELED THE BGR TO ATL PORTION. UNFORTUNATELY; WE DID NOT NOTICE OUR LOSS OF ABILITY UNTIL AFTER TKOF. THIS INCIDENT WAS DIRECTLY RELATED TO FATIGUE. INTL LONG HAUL FLTS SHOULD PROVIDE FOR A MINIMUM IN HOTEL REST OF AT LEAST 10 HRS.