(A) The Board of Trustees shall have the power to pass ordinances:
(1) To prevent and remove nuisances within the village or within its one-mile zoning jurisdiction;
(2) To restrain and prohibit gambling;
(3) To provide for licensing and regulating theatrical and other amusements within the village;
(4) To prevent the introduction and spread of contagious diseases;
(5) To establish and regulate markets;
(6) To erect and repair bridges;
(7) To erect, repair, and regulate wharves;
(8) To regulate the landing of watercraft;
(9) To provide for the inspection of building materials to be used or offered for sale in the village;
(10) To govern the planting and protection of shade trees in the streets and the building of structures projecting upon or over and adjoining, and all excavations through and under, the sidewalks of the village;
(11) To maintain the peace, good government, and welfare of the village and its trade and commerce; and
(12) To enforce all ordinances by inflicting penalties upon inhabitants or other persons for violation of such ordinances, not exceeding $500 for any one offense, recoverable with costs.
(Neb. Rev. Stat. § 17-207)
(B) The village has the power and authority by ordinance to define, regulate, suppress, and prevent nuisances, and to declare what constitutes a nuisance, and to abate and remove the same. The village may exercise this power and authority within its corporate limits and extraterritorial zoning jurisdiction.
(C) The village may enter into an interlocal agreement pursuant to the Interlocal Cooperation Act with a county in which the extraterritorial zoning jurisdiction of the village is located to provide for joint and cooperative action to abate, remove, or prevent nuisances within such extraterritorial zoning jurisdiction. The governing body of such village and the county board of such county shall first approve such interlocal agreement by ordinance or resolution.
(Neb. Rev. Stat. § 18-1720)