Neb. Rev. Stat. §§ 16-217
A city of the first class by ordinance may provide for the removal of elective officers of the city for misconduct. The city may create any office that it deems necessary for the good government and interest of the city. The city may provide for filling vacancies which occur in any elective office, except the mayor or member of the city council, by appointment by the mayor with the consent of the city council to hold his or her office for the unexpired term. Whenever the city council fails to consent to any appointment made under this section by the mayor by the close of the second regular city council meeting following the announcement of the appointment, the vacancy shall be filled by a special election to be held as prescribed by ordinance in the ward in which such vacancy exists. A vacancy in the office of the mayor or on the city council shall be filled as provided in section 32-568.
Neb. Rev. Stat. §§ 16-217