Neb. Rev. Stat. §§ 49-14,107
If a political party other than a legally recognized party shall receive at least five percent of the entire vote of the state at a general election, the membership of the commission shall be increased by one. The additional member shall be appointed by the Governor from a list of at least five individuals who are qualified to serve pursuant to section 49-14,106 and subsection (2) of section 49-14,111 submitted by the state chairperson of the political party receiving such five percent vote and shall be subject to confirmation by the Legislature in the same manner as the other appointed commissioners are selected and confirmed. If two or more of the individuals whose names appear on such list submitted to the Governor are unwilling to withdraw from activities or resign from positions as required by section 49-14,114, the Governor shall follow the procedure prescribed in section 49-14,112. Should any political party fail to poll at least five percent of the entire vote of the state at a general election, the position of that party shall be terminated, except that any person serving as a member may serve to the end of that person's term.
Neb. Rev. Stat. §§ 49-14,107