A B767 Captain reported the flight attendant crew on the inbound aircraft turned around on his outbound flight but because of a previous maintenance delay would be on duty for 17.5 hours at the destination and were so fatigued they were unsafe.

Narrative

Our outbound flight was delayed for five hours due to inbound\mechanical delay from its originating station. The flight attendants do a turn so inbound flight attendants are the outbound flight attendants. I figured that since the flight was so late they had re-crewed the flight. They had not; during the flight I found out from the flight attendants that the crew desk had asked the flight attendants to waive. The flight attendants had been on duty since midmorning; so they had already been on duty without rest at our departure time of almost 13 hours. With a scheduled arrival after midnight this means they would have been on duty over 17 and 1/2 hours! I don't know the FAR's for flight attendants but they insisted this was legal and it was obvious they were scared of the crew desk. Their fatigue factor was very high; and they were obviously struggling to stay awake. My concern as a Captain is if an emergency developed during the flight that my cabin crew would not be able to perform due to fatigue. At times when I would talk with the cabin crew during the flight they were almost incoherent and struggling to understand what I was telling them; they were so tired. This is a definite safety factor.