FATIGUED FLT CREW OVERFLIES CLEARANCE BY 25 MILES BEFORE BEING CONTACTED ON GUARD BY ACR FLT CREW TO REESTABLISH COMS WITH ATC.

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I WAS GIVING IOE COPLT TRAINING AT THE TIME. WE HAD BEEN UP ALL NIGHT AND WERE ON A SECOND TRIP. WE WERE CLRED DIRECT TO DJB AND THE COPLT PUT DJB IN THE GPS AND WE WERE GOING DIRECT. I WAS HAVING TROUBLE KEEPING MY EYES OPEN AND TOLD THE FO TO GET THE RADIOS FOR ABOUT 10 MINS WHILE I CLOSED MY EYES. (UP ALL NIGHT; SECOND TRIP.) WHEN I WOKE UP; I NOTICED WE WERE GOING DIRECT TO MARGN INTXN AND THE FO SAID WE WERE GOING TO MARGN. I PULLED OUT THE APCH PLATES FOR FNT AND GOT THE ATIS AT FNT. THEN I LOOKED AT THE GPS FOR OUR DME FROM MARGN AND SAW THAT WE WERE 12 MI N OF MARGN (WE HAD ALREADY PASSED MARGN). I TOLD THE FO WE WERE PAST MARGN AND I TOOK THE CTLS AND TURNED DIRECT TO FNT. THE NEXT THING I HEARD WAS AIRLINE CALLING US ON 121.5 TO CONTACT ATC AND I DID THAT. ATC TOLD ME THEY HAD BEEN TRYING TO CALL US ON SEVERAL FREQS AND ASKED US IF WE WERE ON A HDG OR DIRECT TO MARGN INTXN BECAUSE WE HAD GONE 25 MI N OF MARGN INTXN THEN TURNED TOWARD FNT. I ASKED THE FO IF HE HEARD ATC AND HE SAID HE HAD NOT HEARD FROM ATC FOR A WHILE. I TOLD ATC THIS AND SHE GAVE ME A PHONE NUMBER TO CALL WHEN WE LANDED IN FNT. I TALKED TO THE FO ON THE GND AND ASKED HIM ABOUT THE LOST COM AND HE SAID ATC DID NOT CALL HIM. ALSO HE SAID WE WERE GOING DIRECT TO MARGN AND HE JUST MISSED WHEN WE HAD PASSED IT. HE WAS VERY TIRED AND I THINK HE DID NOT REALIZE THE SHORT TIME IT WAS GOING TO TAKE TO CROSS MARGN. DISCOVERED: I DISCOVERED THAT WE HAD CROSSED MARGIN. CORRECTIVE ACTIONS: I TOOK THE CTLS AND TURNED TOWARD FNT. CONTRIBUTING FACTORS: 1) BOTH OF US WERE VERY TIRED AT THE TIME FROM BEING PAGED OUT AT XA00 THE NIGHT BEFORE AND THIS MAY HAVE AFFECTED THE FO'S SENSE OF TIME IT WOULD TAKE TO CROSS MARGN INTXN. 2) THE FO WAS IN TRAINING AND SHOULD HAVE WOKE ME UP 150 MI OUT FROM FIX SO I COULD WATCH AND GET READY FOR THE ARR PROCESS. HE WAITED WAY TOO LONG AND I TOLD HIM THIS. 3) I BELIEVE THAT WE HAD FLOWN OUT OF CTR'S RADIO RANGE AND THAT IS WHY WE NEVER HEARD ATC CALL. THE NEXT DAY WE HEARD ATC LOOKING FOR ANOTHER PLANE. THIS TELLS ME MAYBE ZOB MIGHT HAVE A PROB IN THE AREA 50-100 MI S OF MARGN INTXN. HUMAN PERFORMANCE: FATIGUE PLAYED A HUGE FACT IN THIS SITUATION. I WISH THAT THERE WERE FLT RULES PREVENTING A PLT FROM BEING ON CALL 24 HRS A DAY WITHOUT ONLY 1 IN 7 DAYS OFF. WE ARE A PART 121 SUPPLEMENTAL CARRIER WITH A NON-SCHEDULE FOR TRIP -- CAN BE CALLED OUT AT ANY TIME DAY OR NIGHT. IF I WAS NOT SO TIRED I COULD NOT KEEP MY EYES OPEN; I WOULD HAVE HEARD ATC CLR US TO MARGN; SAW US CROSS IT AND WATCH THE FO MAKE THE TURN. I ALSO LEARNED THAT IT IS VERY IMPORTANT FOR A CREW MEMBER TO MAKE SURE BOTH CREW MEMBERS ARE ALERT AT LEAST 150 MI OUT FROM DEST. OUR COMPANY'S TRIPS ARE NOT SCHEDULED AND THE PLTS CARRY PAGERS 24 HRS A DAY. IT IS VERY HARD TO WORK THIS KIND OF SCHEDULE AND FATIGUE IS ALWAYS A WORK HAZARD. THE FO'S JUDGEMENT TO NOT WAKE ME UP EARLIER; INACTION TO SEE WE CROSSED OUR FIX; AND TO NOT REALIZE HE HAD NOT HEARD ATC; ALL CONTRIBUTED TO THIS.