Opinion polls suggested the race between right-wing Freedom Party candidate Norbert Hofer and former Greens leader Alexander van der Bellen will be close-run.
Mr Hofer caught everyone by surprise when he scored 35% in a resounding first-round victory.Support for the 45-year-old aviation engineer has been buoyed by a migration crisis that has heightened fears about employment and security
Mr Hofer could give the far-right real power in a western European country and confirm a trend of anti-establishment parties stamping on liberal traditions across the continent.If Mr Hofer wins, he has threatened to dismiss the government coalition of Social Democrats and centrist People's Party if it fails to heed his repeated calls to do a better job.
With his party now outpolling the main groupings in popularity, he could be tempted to dismiss the power-sharing administration in order to give the Freedom Party the chance to win an ensuing election.
But his rival, an economics professor, could also upend the traditionally cosy relationship between Austrian presidents and governments.
Running as an independent, Mr Van der Bellen, 72, has said he would not swear in a Freedom Party chancellor even if that party wins in the next elections, which have to take place within the next two years.
That, too, could create political upheaval and uncertainty that has so far not been seen in post-war Austria.
The president traditionally plays a largely ceremonial role but swears in the chancellor, can dismiss the cabinet and is commander in chief of the military.
