Both states are led by the country's main opposition Union bloc, made up of the Christian Democratic Union and the Bavaria-only Christian Social Union.
In Hesse, they give the CDU a double-digit lead in a three-way contest for the governor's office among the conservative party, Scholz's center-left Social Democrats and the environmentalist Greens.
Scholz's government also faces intense pressure to reduce the number of migrants arriving, a major issue in the run-up to the elections.
Green challenger Tarek Al-Wazir, currently the deputy governor to conservative incumbent Boris Rhein, also faces an uphill struggle.
In Bavaria, governor Markus Soeder is calling for voters to back "continuity and stability."
Persons:
Chancellor Olaf Scholz's, Scholz, —, Karl, Rudolf Korte, Nancy Faeser, Tarek Al, Wazir, Boris Rhein, Markus Soeder, Soeder, Hubert Aiwanger, Aiwanger —
Organizations:
Sunday, Union, Christian Democratic Union, Christian Social Union, CSU, CDU, Social Democrats, environmentalist Greens, Germany, Greens, Free, Welt, Sonntag, Voters, Free Democrats, Free Voters
Locations:
Bavaria, Hesse, Frankfurt, Scholz's