Neb. Rev. Stat. §§ 32-401
The statewide primary election shall be held on the first Tuesday after the second Monday in May in even-numbered years. The statewide primary election shall be held for the purposes of (1) nominating all candidates to be voted for at the statewide general election except (a) candidates who were unopposed at the primary election and not required to be on the ballot and (b) candidates who petition on the ballot or are nominated by their political party, (2) electing delegates to the county, state, and national political party conventions, if applicable, (3) in each presidential election year, voting on a preference for President of the United States, and (4) electing officers in political subdivisions which hold their general elections at the time of the statewide primary election.
Neb. Rev. Stat. §§ 32-401