Texas Local Government Code - LOC GOV'T § 22.034. Initial Election and Term of Office

(a) If the municipality is divided into wards, at the initial election for officers of the municipality, the mayor and the two aldermen from each ward shall be elected. The aldermen for each ward are the candidates from that ward who receive the highest and second highest number of votes at the initial election.

(b) The two aldermen elected from each ward shall draw lots at the first regular meeting of the governing body of the municipality to determine which alderman serves for one year and which alderman serves for two years after the initial election. At each following annual election, one alderman shall be elected from each ward for the regular term.

(c) If the municipality is not divided into wards, the governing body by ordinance may determine the number and the manner of deciding which aldermen elected at the initial election for officers serve for one year and which serve for two years.

(d) If the aldermen of the governing body of a municipality are not serving staggered terms of office as provided by Subsection (c), the governing body by majority vote may establish staggered terms by requiring the aldermen to draw lots.