And if the Social Democrats end up in another grand coalition with Ms. Merkel, as they have done for the past four years, suddenly the official opposition, with all its perks and funding, could be the far-right AfD.
Some 73,500 polling stations across 299 constituencies opened at 8 a.m. and close at 6 p.m. The first predictions from exit polls will be released soon afterward, and the first official results will arrive sometime around 8 p.m. (2 p.m. Eastern).
Germany’s president, Frank-Walter Steinmeier, warned the 61 million Germans eligible to vote not to stay at home and let others decide the future of their country.
“It has perhaps never been as clear that the elections are about the future of democracy and Europe,” he wrote in the mass-market newspaper Bild am Sonntag, amid polls showing that as many as a third of Germans were undecided.
“If you don’t vote, others decide,” Mr. Steinmeier wrote.
On Sunday, #gehtwaehlen, German for “Go Vote,” was trending on social media, as Germans posted images and comments about casting their ballots in an effort to urge their peers to join them.
Germany has a complicated system of proportional representation, in which each voter casts one ballot for their local representative and one ballot for a political party. Those elected locally get their seats. But the parties’ overall share of seats in Parliament is determined by the percentage of second votes they win.
So a low turnout — it was more than 71.5 percent in 2013, less than 1 percentage point more than the record low of 70.8 percent in 2009 — clearly benefits smaller parties, whose supporters tend to be more fervent and ideological.
The Alternative for Germany and The Left are expected to do well in the states that were part of the communist east before Germanreunification in 1990. In the west, North Rhine-Westphalia, Germany’s most populous state, voted this year for a Christian Democrat-led government, ousting the Social Democrats. But no single state functions as a reliable bellwether for Germany.
Though initially reluctant to run for a fourth term, Ms. Merkel has thrown herself into the campaign, especially as the government has brought some order to the chaos engendered in 2015 when she threw the country’s borders open to refugees and migrants.
But the backlash over the migrant crisis, coupled with her long period in office and the wishy-washy nature of grand coalition politics, has led to more support for the more extreme parties like the AfD and The Left, the inheritor of the East German Communist Party.
The coalition has also made it difficult for the new leader of the Social Democrats, Martin Schulz, to differentiate himself from Ms. Merkel.
But he has warned explicitly against an AfD vote, on Friday calling the party “gravediggers of democracy.”
Getting out the vote emerged as a popular theme in final weeks of the campaign, with Ms. Merkel using her rallies first to call on people to vote, and only then asking for their support.
An INSA poll published by the newspaper Bild on Saturday suggested that support was slipping for Ms. Merkel’s conservatives, who dropped two percentage points to 34 percent, and the Social Democrats, down one point to 21 percent.
The AfD rose two percentage points to 13 percent in the poll, putting it on course to be the third-largest party, just ahead of The Left.
The liberal Free Democrats and the leftist Greens are also expected to get more than 5 percent of the vote, the threshold to get seats in Parliament.
That fragmentation would make it difficult for Ms. Merkel to cobble together a coalition, especially if the Social Democrats prefer to remain outside government. Coalition negotiations normally take weeks, if not months, in Germany.
In a separate vote in Berlin of interest to anyone who has ever flown into the city, Berliners are being asked whether to keep the small, convenient, Cold War-era airport, Tegel, even after the planned opening of the much-delayed new international airport farther from the city center town. The delays are widely mocked in Germany and abroad.
Although the referendum is nonbinding, voter support combined with numbers — this year, through July, Tegel has handled some 35 million passengers — could be enough to force politicians to reconsider its planned closing.
In Dresden, Gert Frülling, 75, a retiree, declined to divulge his party preference, but made it clear that he was sympathetic to some of the Alternative for Germany’s proposals.
“It all happened too fast,” he said, referring to the time after reunification. “Dresden is a city of bureaucrats and soldiers, and they dumped all this multiculturalism on us at once. I know we had to change, but it should have happened more gradually.”
He said it would be wrong for other parties to refuse to work with the AfD in Parliament.
“If they present good ideas,” he said, “I think it’s not fair to boycott them.”
In Neustadt, a gentrifying area of Dresden, Rebecca Klingenburg, 20, was clearly excited to be one of an estimated three million first-time voters.
“One gets to decide on what country one wants to live,” she said.
A mechanical-engineering student, Ms. Klingenburg said she was voting to maintain Germany’s orientation toward Europe, at a time of rising nationalism. “I learned four languages in school,” she said. “I want to make sure that we stay internationally oriented.”
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