Tex. Local Government Code § 23.026: REGULAR TERM OF OFFICE.

(a) The mayor, aldermen, and marshal of the municipality are elected for a term of one year unless a longer term is established under Subsection (b) or under Article XI, Section 11, of the Texas Constitution.

(b) In lieu of one-year terms of office, the governing body may provide by ordinance for two-year staggered terms of office for the mayor and aldermen. If the governing body adopts the ordinance, the mayor and two aldermen serve for a term of two years. The two aldermen who serve two-year terms are determined by drawing lots at the first meeting of the governing body following the annual municipal election held after the ordinance is adopted. The remaining aldermen hold office for an initial term of one year. Thereafter, all members of the governing body serve for a term of two years.

Acts 1987, 70th Leg., ch. 149, Sec. 1, eff. Sept. 1, 1987.