Austrians are going to the polls - with the very real prospect of electing the EU's first far-right head of state.
Norbert Hofer of the anti-immigrant Freedom Party is taking on Alexander van der Bellen, who is backed by the Greens.
Mr Hofer topped the first-round vote but fell well short of an outright majority.
For the first time since WWII, both the main centrist parties were knocked out in the first round, amid concerns over Europe's migrant crisis with 90,000 people claiming asylum in Austria last year.
While the presidency is a largely ceremonial post, the president has powers to dismiss the government.
And a Hofer victory could be the springboard for Freedom Party success in the next parliamentary elections, scheduled for 2018.
Polls opened at 7am (5pm NZ time) and were set to close at 7pm.
Postal ballots, which could be crucial if the result is close, would be tallied on Monday.
In the first round, Mr Hofer, 45, secured 35 percent of the votes, while Mr Van der Belle polled 21 percent.
Such was the political shock at the far right's first-round win that Chancellor Werner Faymann resigned after losing the support of his Social Democratic party colleagues.
The Social Democrats and the People's Party have governed Austria for decades, either alone or in coalition.
At the last general election in 2013, they together won just enough votes to govern in a "grand coalition".
At his final election rally on Friday in Vienna, Mr Hofer, 45, sought to hammer home his message that immigrants needed to integrate.
"Those people who respect and love Austria and have found a new home here are warmly welcome," he said to applause.
"But those, it has to be said, those who do not value our country, who fight for Islamic State, or who rape women, I say to these people: this is not your homeland. You cannot stay in Austria."
The presidents of the European Commission and the European Parliament, Jean-Claude Juncker and Martin Schulz, both of whom expressed concern that Mr Hofer could win.
"I say to them very politely but firmly: we don't take orders from Brussels or Berlin," Mr Hofer said at the rally.
Mr Van der Bellen told his final rally in Vienna that it was likely to be a close race.
"I think it could be on a knife edge - 50-50 who will win, so this time, as with previous votes, but more than ever for this important election, every vote will count," he said.
At a news conference, he reflected: "As you know, I am 72 years old and I've experienced how Austria rose from the ruins of World War II, caused by the madness of nationalism."
The two rivals had engaged in an angry TV debate earlier in the week, described as "political mud-wrestling" by commentators.
Incumbent President Heinz Fischer, 77, could not run again after two terms in office.