Wyo. Stat. Ann. § 15-11-201

At the first meeting of the council after the first election in a newly incorporated city or town, other than a first class city or municipality adopting the city manager or commission form of government, two (2) of the councilmen first elected shall be selected by lots to serve four (4) year terms and two (2) to serve two (2) year terms. At each subsequent general election, two (2) councilmen shall be elected to serve a four (4) year term.