Opinion polls in the key state of North Rhine-Westphalia suggest an emphatic re-election victory for the centre-left Social Democrats (SPD).
Analysts say voters look set to reject Angela Merkel’s tough line on fiscal discipline as a cure for state debt.
Recent polls in Greece, France and Italy have rejected austerity policies.
Voting in North Rhine-Westphalia ends at 16:00 GMT, with exit polls expected soon after.
The CDU and its national coalition partner, the Free Democrats, recently lost elections in the northern state of Schleswig-Holstein. The CDU scored its lowest tally in the state for 50 years.
The poll in North Rhine-Westphalia (NRW) will test the popularity of Chancellor Merkel’s CDU, as opposition to her strict austerity policies grows outside Germany.
NRW, Germany’s most populous state and with a large economy, has a history of influencing national politics.
The election was called in March after the state’s minority government, run by a coalition of the SPD and Greens – narrowly failed to get a budget passed.
Despite its troubles, polls suggest that state premier and SPD candidate Hannelore Kraft – who has headed the fragile government for the past two years – will easily defeat CDU rival Norbert Roettgen, who is Angela Merkel’s environment minister.
In her campaign, Hannelore Kraft has emphasized strengthening indebted local communities, investing in education and boosting the state’s business appeal.
Norbert Roettgen, on the other hand, has accused the SPD of financial irresponsibility, holding rallies dominated by a huge inflatable “debt mountain”, to emphasize the state’s problems.
He provoked controversy early in the campaign by refusing to commit to being a full-time opposition leader if he lost. Such a move would cost him his job in Berlin.
Angela Merkel said the election offered the region an opportunity to elect a government that would not take on “ever more debt”.
The Pirate Party, which has grown in strength recently with its calls for transparency and internet freedom, is looking to enter its fourth state parliament.
Nationally, Sunday’s election will not change the balance of power, whatever the outcome.
But opposition leaders warned it could send an important signal ahead of national elections expected in late 2013.
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