While the airport remains open, passengers are being referred to their specific airline for further updates and information about their flights.
A Manchester Airport spokesperson said the issue had been resolved at 03:00 BST and that "most scheduled flights" would be operated as planned on Monday.
"However, we expect that there will be a small number of delays and cancellations as a result of the issues experienced," the spokesperson told BBC News.
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The disruption is set to continue on Monday. The Manchester Evening News reported that some of those left stranded had already boarded their planes and were made to wait for two hours on grounded aircraft.