"Hackers have accessed tens of thousands of British Airways frequent flier accounts.
The airline said no personal information has been viewed or stolen, and it has frozen affected accounts for the next day or so while it resolves the issue.
It means top executive club fliers may not be able to use their air miles until the issue is resolved.
Airline chiefs said only a small proportion of its millions of customers are affected, and that their names, addresses, bank details and other personal information have not been accessed.
The company apologised to customers and said it expects to have the system back up and running in the next day or so.
It is not known who is behind the hack, but it is believed it was carried out by an automated computer programme looking for chinks in the armour of the company's online security systems.
A British Airways spokesman said: "British Airways has become aware of some unauthorised activity in relation to a small number of frequent flyer executive club accounts.
"This appears to have been the result of a third party using information obtained elsewhere on the internet, via an automated process, to try to gain access to some accounts.
"We would like to reassure customers that, at this stage we are not aware of any access to any subsequent information pages within accounts, including travel histories or payment card details.
"We are sorry for the concern and inconvenience this matter has caused and would like to reassure customers that we are taking this incident seriously and have taken a number of steps to lock down accounts so they can no longer be accessed.""
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