Flight 5501 landed safely about 9 p.m. after arriving from Washington, DC., but while taxiing to the gate, it rolled into the mud.
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There were 19 passengers on board and there were no reported injuries, RDU officials said.
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The passengers were being transported to Terminal 2.
RDU said the runway reopened shortly before 10:30 p.m., allowing flights to resume landing and departing the airport.
Several incoming planes were diverted as a result of the incident.
According to RDU officials, the Delta aircraft was safely towed to a remote area Saturday afternoon. Wake County Sheriff Gerald Baker said the plane was not damaged.
Travelers have been advised to check with their airline for flight status before going to the airport. Officials ask that any additional questions be referred to the airline.
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