The winnner of the run-off election will lead the Eastern European country into the European Union on January 1, 2007.
Georgi Parvanov, the incumbent president, a 49-year-old historian, won the first round on October 22 with 64 per cent of the vote.
His rival, Volen Siderov, a 50-year-old journalist, took 21.5 per cent.
More than 6.4 million people are eligible to vote.
Parvanov’s support is 73 per cent according to a pre-election poll conducted by the national centre for public opinion research.
The same poll put Siderov on 24 per cent.
A ceremonial role
Going into the runoff, most of the country’s mainstream parties, including the governing Socialists, have given their backing to Parvanov, who is running as an independent.
The presidency is a largely ceremonial position, while the real power rests with the prime minister and parliament.
The president does however have legislative veto power.
Polls open at 6pm (0400 GMT) and close at 7pm.
Initial projections are expected on Sunday evening and final results on Monday.