The incidents were uncovered through a Freedom of Information request submitted to the Civil Aviation Authority by The Sun in Britain.
The authority declined to name the airlines involved in the incidents, saying it would breach confidentiality, The Sun reported.
In one occurrence, the captain left the cockpit momentarily and got no reply from his first officer when he tried to call him on a radio link. When the captain returned, he found the first officer "slumped over the controls," the documents said.
In the second incident, a captain returned to the cockpit to find his first officer was asleep and had to be shaken awake, The Sun reported.
The British Airlines Pilots Association said 43 percent of members polled admitted to sleeping in the cockpit. A third of those said they woke to find the other pilot also asleep.