There are 2 US Post Offices in Nance County serving a total of 3,362 residents equating to 1,681 residents per post office. It's estimated that approximately 5,366 packages are handled across the 2 county post offices annually. Nance County is a county in the U.S. state of Nebraska. As of the 2010 census, the population was 3,735. Its county seat is Fullerton. In the Nebraska license plate system, Nance County is represented by the prefix 58 (it had the fifty-eighth-largest number of vehicles registered in the county when the license plate system was established in 1922)."