In a statement posted on the Atlanta-based airline's website at 11:45 p.m., CEO Ed Bastian apologized to customers who were impacted by this "frustrating situation."
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Delta tweeted that its I-T systems are returning to normal, but about 150 flights have been cancelled and more are expected Monday.
Video posted on Twitter showed passengers at a terminal at LaGuardia at a standstill as they wait for the outage to end.
Bastian says this type of disruption "is not acceptable to the Delta family who prides itself on reliability and customer service."
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Delta says a waiver has been issued for travel scheduled on Jan. 29 and 30, for rebooking by Feb. 3.
In August, Delta suffered a computer breakdown after a power outage in its operations center. The airline canceled more than 2,000 flights over three days.
(The Associated Press contributed to this report.)