Park rangers say 58-year-old Kevin Lynch was last seen Saturday walking along the boundary of the park at a North Carolina resort.
They believe he may be confused about where he is.
Officials say search operations remain limited to a select number of trained personnel as the search zone is in a remote area of the park full of dense vegetation and difficult terrain.
Lynch is from Woodbridge, New Jersey, and is described as 5 feet 5 inches tall with brown hair and brown eyes. He was last seen wearing brown cotton shorts, a brown shirt with a deer on it and a camouflage baseball cap.
Anyone who sees him is asked to call Great Smoky Mountains National Park dispatch at (865) 436-1230.
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