ACR FLT CREW RPTS BEING RESCHEDULED TO ESSENTIALLY FLY 2 RED EYE FLTS IN A ROW; AND THE PROBS ENCOUNTERED DUE TO FATIGUE.

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RECEIVED A CALL FROM CREW SCHEDULE FOLLOWED BY DISPATCH BOTH ADVISING OF DELAY ON FLT FROM WEST COAST TO HNL. NEW DEP TIME WAS PLANNED AT XA00 FOR LATE ARRIVING EQUIP. DEP TIME WAS SUBSEQUENTLY REVISED TO XA40. HAD COMPLETED THE SAME SEGMENT THAT MORNING; AND WAS NOT TOO KEEN ABOUT DOING ANOTHER ONE. ONLY ABLE TO SLEEP FOR APPROX 6 HRS (XJ00-XP00 LCL) AFTER ARRIVING FROM HNL THAT MORNING. BOTH THE FO AND I WERE TIRED AT DEP TIME AND DISCUSSED THE LEGALITIES OF THE ASSIGNMENT; BUT COULD NOT DETERMINE IF IT WAS CONTRACTUALLY LEGAL OR NOT. LAST HR OF FLT WAS VERY DIFFICULT AND I VERY NEARLY DOZED OFF WHILE ON VECTORS FOR THE ILS RWY 4R APCH AT HNL. FO WAS CONFIGURED AT FLAPS 20 DEGS AND 160 KIAS PASSING THE PERLY FAF. SOME POINT AFTER THAT HE CALLED FOR FLAPS 25 DEGS; AND I REALIZED THE LNDG GEAR WAS NOT DOWN. I TOLD HIM HE NEED THE GEAR FIRST OR WE'D GET A HORN. HE IMMEDIATELY CALLED FOR THE GEAR; AND AS IT WAS EXTENDING WE DSNDED BELOW 800 FT AGL AND GOT THE EGPWS GEAR WARNING. I MADE THE 1000 FT CALL (ALSO MISSED DUE TO FATIGUE); AND BY 500 FT AGL WE WERE FINALLY CONFIGURED FOR LNDG; WHICH WAS UNEVENTFUL. THIS DELAY CAUSED US TO OPERATE 2 CONSECUTIVE FLTS INTO THE WINDOW OF CIRCADIAN LOW; WITH PREDICTABLE RESULTS. WHY WE WOULD NOT ALLOW THIS ON A SCHEDULED BASIS; BUT PERMIT IT IN THE ACTUAL OP; IS BEYOND ME. IN OTHER WORDS; IT'S NOT LEGAL TO PRINT IT; BUT IT IS LEGAL TO ATTEMPT TO FLY IT; IS THAT WHAT WE'RE SAYING? LET'S GET REAL HERE BEFORE WE HAVE ANOTHER INCIDENT OR WORSE. MY NEW STANDARD IS NO CONSECUTIVE DUTY PERIODS INTO THE WINDOW OF CIRCADIAN LOW PERIOD.