Ukrainians are voting in a presidential election run-off, after a bruising campaign and warnings of mass street protests and demonstrations.PM Yulia Tymoshenko and opposition leader Viktor Yanukovych are competing for the top job after President Viktor Yushchenko lost out in the first round.
Both camps have accused each other of plotting to rig the vote.
Some analysts are predicting a close race, saying the losing side would most likely challenge the poll's results.
Mr Yanukovych won last month's first round of voting, finishing 10% ahead of Mrs Tymoshenko.
'Beautiful' Ukraine
Voting so far appears to be proceeding smoothly, says the BBC's Richard Galpin in Kiev.
The election commission says all polling stations opened on time and both candidates have cast their votes.
Election observers say they expect a higher turnout than during the first round.
After casting her ballot, Mrs Tymoshenko said she had voted for "a new Ukraine - a happy Ukraine, a wealthy, beautiful, European state".
And one of her supporters, Vladimir Khivrenko, said he was voting "against the return of our Soviet past".
"Tymoshenko has promised us a new path to Europe, and I believe her," he said, quoted by the Associated Press news agency.
But one of Mr Yanukovych's supporters said she wanted stability and order.
"Yanukovych offers us the guarantee of a normal life," Tatyana Volodaschuk said.
My Yanukovych himself said the election would mark the first step in overcoming Ukraine's crisis.
"The people of Ukraine deserve a better life, so I voted for positive changes, stability and a strong Ukraine," he said.
Sunday's vote came after a bitter mud-slinging campaign where real policy issues and debate appeared to have been forgotten, says our correspondent Kiev.
On Saturday, Mrs Tymoshenko's political bloc accused Mr Yanukovych's Party of Regions of blocking its supporters from overseeing the vote in the eastern Donetsk region - the opposition's stronghold.
"The main plan of the Yanukovych team for success in the election is deceit, criminal schemes and violations of citizens' rights," the prime minister's bloc said in a statement.
Mrs Tymoshenko earlier threatened to take her supporters to the streets if she was defeated in the poll, saying the protests could be larger than those of the 2004 Orange Revolution, which swept Mr Yushchenko to power.
Mr Yanukovych's camp hit back with allegations that some supporters of the prime minister had been tampering with ballots in an attempt to get votes from eastern Ukraine disqualified.
"Nobody would have thought that one of the sides in the election process would stoop to such cynicism," said Mr Yanukovych's campaign manager Mykola Azarov.
Most analysts believe the result of Sunday's election will be close - though some think Mr Yanukovych will win, our correspondent adds.
If that is correct it would be a remarkable comeback for the man who as the representative of the old regime five years ago was swept aside by the Orange Revolution.
But analysts say there is also a significant number of voters who will only make up their minds at the last moment, or, who will not vote at all.
Mr Yanukovych initially thought he had won the presidential election in 2004. But amid mass protests, the Supreme Court ruled the vote had been rigged.
At that time he clearly enjoyed the full backing of the Russian government.
But this time he has indicated he will be more pragmatic, looking both east and west, and saying he wants Ukraine to be integrated into the European Union, our correspondent adds.
