Thousands of American Airlines' flights over the Christmas period have no pilots assigned to them after a computer glitch gave time off to too many cockpit crew.

The union for the pilots says that possibly as many as 15,000 flights between 17 and 31 December will not have adequate crew numbers.

Bloomberg reported that flights affected are from Dallas, Boston, Miami, New York City, Philadelphia, Salt Lake City and Charlotte.

The Allied Pilots Association (APA) said it was told about the problem last week, with one spokesman saying: "It's a really bizarre situation".

To get the required cover over the busy holiday period, the airline will offer pilots 150 per cent of their hourly pay although this has been opposed by the union which says it violates its labour pact.

APA spokesman Dennis Tajer said another solution would be needed for pilots to give up their planned holidays.

"This is certainly not routine. This is a crisis right now, and in that crisis, they've gone solo," he said.

John Cox, chief executive officer of consultant Safety Operating Systems said that at the least the airline would have to pay the crew more but he did not think there would be mass cancellations.

"There's going to be a lot of midnight oil spent on it, but I think they'll get the vast majority of them covered one way or another."

American Airlines spokesman Matt Miller told Bloomberg: "We are working through this to make sure we take care of our pilots and get our customers to where they need to go over the holidays," Miller said.