Neb. Rev. Stat. § 81-15,171

The citizen members of the board shall be appointed for terms of six years, except that of the members first appointed, except directors of agencies, the terms of three shall expire at the end of the second year, three at the end of the fourth year, and three at the end of the sixth year, as designated at the time of appointment. Any member appointed to fill a vacancy occurring prior to the expiration of the term for which his or her predecessor was appointed shall be appointed for the remainder of such term. A vacancy on the board shall exist in the event of the death, disability, or resignation of a member. All members shall be reimbursed for expenses as provided in sections 81-1174 to 81-1177 .