Polling stations across Germany's two states are scheduled to open at 8 a.m. local time (6 a.m. GMT).
In Thuringia, the AfD is widely expected to emerge as the largest party.
Meanwhile, the SPD, Greens and Freedom Party's coalition partners are doing so poorly in Thuringia that they may not even win a single seat in the state parliament.
The AfD is officially classified as a right-wing extremist group in Thuringia, where its controversial leader, Björn Höcke, was recently fined for using Nazi slogans, a charge he denies.
In Saxony, the AfD is competing with the CDU for first place.
Last week's stabbing attack in western Germany, in which a Syrian asylum seeker and suspected Muslim was accused of killing three people, sparked fierce criticism of how previous governments handled immigration.
Even if the AfD emerges as the largest party in both states, that does not mean it will take power, as other parties have publicly ruled out cooperating with it to win a majority of seats.
Nonetheless, the poll results will be seen as a touchstone ahead of Germany's 2025 federal elections.
