The Missouri General Assembly is the state legislature of the U.S. state of Missouri. The bicameral General Assembly is composed of a 34-member Senate, and a 163-member House of Representatives.Members of both houses of the General Assembly are subject to term limits.Senators are limited to two four-year terms, and representatives to four two-year terms; a total of 8 years for members of both houses.he bicameral General Assembly is composed of a 34-member Senate, and a 163-member House of Representatives. Members of both houses of the General Assembly are subject to term limits.