B777-200 CREW SHOWED FATIGUE AFTER BEING SCHEDULED TO FLY ON THE BACK SIDE OF THE CLOCK.

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I WAS FLYING RELIEF PLT. OPERATING ACR X ZZZZ-SFO ON MAR/TUE/04; THE FLT CREW MISSED SEVERAL RADIO CALLS; HAD DIFFICULTY RECALLING CLRNCS ISSUED JUST MINS BEFORE; AND FAILED TO MAKE A CABIN SECURITY ANNOUNCEMENT IN A TIMELY MANNER. OTHER ERRORS OR OMISSIONS WERE CAUGHT AND RESOLVED BY THE CREW IN THE PRACTICE OF GOOD CRM: QUESTIONING; REVIEWING; REPEATING STEPS AND PROCS. AT NO TIME DID THE CREW ALLOW THEMSELVES TO BE RUSHED. EACH OF THE CREW MEMBERS FELT TIRED. I AM WRITING THIS RPT TO BRING ATTN TO THE SERIOUS DANGERS OF OPERATING ON THE BACK SIDE OF THE CLOCK WITHOUT ENOUGH TIME FOR PROPER REST AND RECOVERY. THE B777 SFO-ZZZZ-SFO IS A LATE DEP FROM SFO AND AN EARLY DEP FROM ZZZZ FOR THE RETURN LEG. EACH DUTY PERIOD OPERATES DURING THE CRITICAL XA00-XF00 BODY CLOCK PERIOD. THIS IS THE ONLY INTL TRIP WHICH OPERATES THROUGHOUT THIS PERIOD ON BOTH LEGS. IN THIS SIT; A PLT MUST BOTH RECOVER FROM AND REST FOR A FULL PERIOD OF BACK SIDE OF THE CLOCK FLYING. THIS REPRESENTS AN ADDITIONAL SLEEP DEFICIT NOT EXPERIENCED ON ANY OTHER INTL TRIP. THE PRESENT LAYOVER DOES NOT ALLOW ADEQUATE TIME TO BOTH REST AND RECOVER. THE OPPORTUNITY FOR AN ADDITIONAL 5-8 HRS OF REST WOULD CORRECT THIS SERIOUS PROB.