Neb. Rev. Stat. § 32-531

After the initial appointments to the county weed district board in counties in which the members are elected, the two members from cities, villages, or townships shall thereafter be elected at the statewide general election in 1994 and each four years thereafter, and the three members from rural areas shall be elected at the statewide general election in 1996 and each four years thereafter. After the initial appointments, the term of each member shall be four years or until his or her successor is elected and qualified. The members shall meet the qualifications found in section 2-953.01 . The members shall be elected on the nonpartisan ballot.