More than a third of Austrian voters have backed far-right candidate Norbert Hofer in the first round of presidential elections.

Here is a look at what this means for the run-off vote between Hofer and Green candidate Alexander Van der Bellen, and how it affects Austrian politics:

Will Austria get its first far-right president?

Freedom Party (FPOe) legislator Hofer still has to win the final election in May, but he enters the race with a big lead over former Green party leader Van der Bellen.

Hofer won 35 per cent of the ballots on Sunday, 14 percentage points more than his rival.

To reverse the trend, Van der Bellen would not only need to win over all voters who backed the social democratic candidate in the first round, but he would also have to appeal to conservative voters, which he has failed to do so far.

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Will Van der Bellen be able to catch up?

Public opinion on one of the key issues in the presidential race, that of an FPOe-led government, is against the 72-year-old economist.

Van der Bellen has said he would not appoint a government that is led by the FPOe, even if the rightists win the next parliamentary election.

However, 80 per cent of Austrians want the president to swear in any government that has a majority in parliament, according to a poll that the Sora institute conducted on Sunday.

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Will Austria also get a far-right government?

Even if the 45-year-old Hofer becomes president, the centrist coalition government led by social democratic Chancellor Werner Faymann would remain in office.

However, Hofer said he might dismiss ministers or the entire cabinet as a last resort if Faymann's team does create jobs, boosts the sluggish economy or implements long-overdue education reforms.

"The government should know that it will get harder for them, but it will get better for Austria," Hofer said.

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What does all this mean for Chancellor Faymann?

Critical voices are mounting from within his own party and from the People's Party (OeVP), which forms the coalition with the Social Democratic Party (SPOe).

Brigitte Ederer, a former leading SPOe official and an influential voice in the party, called for Faymann's resignation. "This defeat has a lot to do with the government's performance," she told the Tiroler Tageszeitung newspaper.

Erwin Proell, the most powerful figure in the OeVP, launched a broadside against Faymann, accusing him of procrastinating on Austria's most pressing problems.

"In the long run this is not good for politics and for the republic," said Proell, the long-time governor of Lower Austria province.

Faymann acknowledged that the election result was a "clear warning" that the government's parties must stop bickering and must focus on delivering results.

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Will Austria shift to xenophobic policies?

It is more likely that the coalition will try to push ahead policies related to economic growth, the labour market and education.

The government now has a "last chance" to improve its performance ahead of the 2018 elections, conservative Vice Chancellor Reinhold Mitterlehner said.

In any case, the current government has already shed its open-border stance and has announced a row of restrictive asylum and border policies in recent months.

A package of amendments that is designed to curb asylum claims is set to pass parliament on Wednesday.

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What might happen in the next parliamentary election?

Another FPOe victory looks likely. The most recent survey from early April shows the rightists in the lead with 31 per cent, ahead of the current coalition parties. The FPOe has dominated surveys for the past year.

However, the FPOe would most likely need to form a coalition with one of the two centrist parties to achieve a majority in parliament.

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