An international Captain described an onerous flight sequence in the Pacific he believed to be unsafe due to cumulative and predictable fatigue.

Narrative

This report concerns a trans-Pacific flight assignment including back to back all night pairings (body clock); two un-augmented inter-Asia segments and 36 hours of flight time. We started the sequence with a 12.7 hour actual flight; single augmented with an hour plus delay on the front end. When we arrived we cabbed to downtown for an additional 1.5 hours on the body before rest. The first internal Asia leg is all night; un-augmented. The return leg is daylight-but all night body time-followed by another 1.5 hour cab ride downtown.The [opportunities for] rest were insufficient to maintain any alertness particularly on the last leg. Both the First Officer and I experienced periods of unintended sleep while at the controls. No amount of coffee or mental discipline was sufficient to stay awake!!! This is unsafe and made more unsafe by requiring: 1. Over 12 hours single augmented on the first leg. 2. Two un-augmented legs on the back side of the clock with long preflight awake hours. 3. Over 8 extra hours of 'duty time' in CABS!!!Rework this trip before someone gets hurt. No one in the cockpit for the last 6 hours was at their peak to respond to irregular situations. We weren't even able to stay awake the whole time in the seat.