It is not known how many flights are affected but passengers have reported issues at a number of airports on social media.
'Catastrophic'
Journalist Martyn Kent said he had been sat on a plane at Heathrow for 90 minutes. He said the captain told passengers the IT problems were "catastrophic".
BA staff in Terminal 5 were resorting to using white boards, according to passenger Gareth Wharton.
Philip Bloom said he had been waiting on board a Heathrow-bound flight at Belfast for two hours.
He added: "We haven't been told very much just that there is a worldwide computer system failure.
"We were told that we couldn't even get on other flights because they are unable to see what flights we can be moved to."
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