The state aircraft exhibited "unusual vibrations in connection with the retraction of the landing gear," the state said in a news release.
Before landing, an indicator light regarding hydraulic pressure came on.
The pilot asked to have emergency equipment standing by on sight for the landing, and the aircraft landed safely at RDU.
Five people were onboard the plane during the incident -- including the governor, a staffer, security, the pilot and co-pilot. No one was injured.