With reference to the posting by MungoP:
In many, many years of flying longhaul with a crew of, at least, 3 on the flightdeck, I never had a problem.
On shorthaul flying at night, I have had two quite surprising events.
On the first one, the F/O (as PNF) called "Outer Marker" on finals. The next call should have been "500 feet" but it didn't come for he had "nodded-off"!
The second event was during an SID from a large European airfield at night. The F/O was PF and when the SID called for a 90° left turn and it didn't happen, I quickly discovered that he had nodded-off as well!
I have often wondered if some of our colleagues make as much use of rest time as they should do.