About 50 contested primaries are being held to determine nominees for the Missouri Legislature.
Three special elections also will fill vacant state House seats and determine whether Republicans hold a supermajority.
The winners of Tuesday's special elections likely will be sworn into office in time for a Sept. 10 session when lawmakers consider whether to override Gov. Jay Nixon's vetoes.
Republicans are favored in two of the three special elections.
They only need to win one to regain a two-thirds majority in the House that would allow them to override vetoes without needing any Democratic votes. Republicans already hold a two-thirds majority in the Senate.
The winners of Tuesday's legislative primaries will advance to the November elections for terms that will begin next January.