The anti-immigration Alternative for Germany has long railed against Chancellor Olaf Scholz's unpopular coalition government, which faces national elections in a year.
In the state election in Brandenburg, the AfD hopes to replicate the strong gains it made in the east three weeks ago, when it won a parliamentary vote in Thuringia and came a close second in Saxony.
A victory in Brandenburg, which surrounds the capital Berlin, would deliver another setback to Scholz's Social Democrats (SPD), the centre-left party that has ruled the state since Germany's reunification in 1990.
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"If the SPD does not come out on top in the elections, it will be a very hard blow for the Social Democrats and Scholz," said Benjamin Hoehne, a political scientist at the Technical University of Chemnitz.
A bruising defeat would mean "the debate about who in the SPD would be the best candidate for chancellor is likely to accelerate", Hoehne added.
Infighting in the government has seen Scholz's approval ratings take a dive while his defence minister, fellow Social Democrat Boris Pistorius, often tops surveys as Germany's most popular politician.
In the long run-up to national elections in September 2025, the opposition conservatives of the CDU-CSU alliance last week selected their party leader Friedrich Merz as their top candidate.
"Not just the people of Brandenburg, all of Germany and beyond are watching this election," Merz said at a final campaign event for the CDU in Potsdam on Saturday.
Islamist attacks
Around 2.2 million people aged over 16 are eligible to vote in Brandenburg. Polls will close at 1600 GMT. The state takes in wealthy towns such as Potsdam, with its Prussian-era Sanssouci Palace, as well as thinly populated rural areas and industrial zones, one of which houses a Tesla plant.
Popular SPD state premier Dietmar Woidke has kept his distance during the campaign from his party colleague Scholz, even though the chancellor's electoral district is Potsdam.
But Woidke, in office for over a decade, has thrown down a challenge to voters by saying he will quit if the AfD wins.
However, the latest surveys give the AfD an edge, predicting it will win with 27-29 percent of the vote, even as the SPD has recently narrowed the gap and polled at 25-26 percent.
Even if it wins, the AfD is unlikely to govern because all other parties have ruled out entering into a coalition with them.
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But their rise has heaped political pressure on Scholz and his governing allies, the Greens and the liberal Free Democrats.
The decade-old AfD has stoked and capitalised on public fears about irregular migration after a string of recent extremist attacks with suspected Islamist motives.
Germany was especially shocked by a knife rampage that killed three people and wounded eight in the western city of Solingen last month.
Police arrested a Syrian asylum-seeker who allegedly claimed allegiance to the Islamic State group and had evaded a deportation order.
Left-wing kingmaker
A recent survey in Brandenburg found that immigration was the top concern for many voters.
"People are always talking about integration and saying that they are not satisfied with what is happening," one voter, Edeltraud Wendland, 82, told AFP on a Potsdam shopping street.
"Of course, we have to help people, but we can't take in too many of them."
The AfD, besides protesting against migrants, Islam and multiculturalism, also questions climate change and holds pro-Russian positions on the Ukraine war.
This year has also seen the emergence of a second populist party, the left-wing Sahra Wagenknecht Alliance (BSW), which is polling at 13-14 percent in Brandenburg.
Hailing from former East Germany, Wagenknecht is a veteran opposition politician and frequent TV talk show guest who quit the hard-left Die Linke party to form her own movement.
She has described the BSW's policies as "leftist-conservative" -- a blend of economic polices that help workers and the poor and conservative cultural positions including on limiting immigration.
As in Thuringia and Saxony, Wagenknecht's party could gain a potential kingmaker role after the election, complicating the task for the other parties who oppose her pro-Russia and anti-NATO stance.
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