Neb. Rev. Stat. §§ 16-401
Regular meetings of the city council of a city of the first class shall be held at such times as may be fixed by ordinance and special meetings whenever called by the mayor or any four city council members. A majority of all the members elected to the city council shall constitute a quorum for the transaction of any business, except as otherwise required by law, but a less number may adjourn, from time to time, and compel the attendance of absent members. When the city council consists of four members as established by ordinance or home rule charter, the mayor shall be deemed a member of the city council for purposes of establishing a quorum when the mayor's presence is necessary to establish the quorum. An affirmative vote of not less than one-half of the elected members shall be required for the transaction of any business.
Neb. Rev. Stat. §§ 16-401