Early official results and exit polls from the re-run of Ukraine's run-off presidential election give opposition leader Viktor Yushchenko a clear lead.
Yushchenko (right) appears to be the more popular of the two Viktors
The original vote, won by Prime Minister Viktor Yanukovych last month, was annulled after widespread fraud.
About 12,000 foreign monitors observed Sunday's repeat election.
Correspondents say the margin of victory will be almost as important as the outcome, in a country with a sharp east-west split.
Source: Ukraine Central Election Commission, with 34% of votes counted
One exit poll suggested that the pro-Western Mr Yushchenko had won by 15 percentage points, and another by 20 points.
Early results from Ukraine's election commission later put his lead at 18 points - although the figure, based on 34% of ballots cast, is expected to change.
Tens of thousands of jubilant opposition supporters, in their distinctive orange colours, gathered in Independence Square in central Kiev late on Sunday.
They celebrated the anticipated victory with a concert and a fireworks display.
Many Ukrainians, going back to the polls for the third time in less than two months, said they wanted to put an end to the country's bitter political crisis .
"Everybody is tired. I am hoping this will be the last round," Lidia Karpenko, 55, told AFP news agency in Kiev.
THIRD TIME AROUND
Repeat of 21 November run-off after cancellation of result
Fourth presidential election since independence in 1991
36 million voters; 12,000 foreign election observers
Public support for Mr Yanukovych is strong in the industrialised east and the south of the country.
However, the candidate once seen as the favourite of the Ukrainian establishment and neighbouring Russia appeared to be preparing for defeat as polls closed.
"If we fail, we will form a strong opposition," he said. Mr Yanukovych, however, has not so far not conceded.
Russian President Vladimir Putin has said he will accept, and work with, whoever wins.
The Ukrainian Committee of Voters, a voters' rights organisation, said in an initial statement it could see no grounds to talk about mass irregularities in Sunday's re-run.
Outgoing President Leonid Kuchma told reporters he hoped this vote would at last determine his successor.
"Dear God, let this be the final vote. I'm sure it will be," he said, suggesting the loser should concede within two days.
Mr Kuchma backed Mr Yanukovych in the earlier vote - but the prime minister had recently attacked the president, presenting himself as an anti-establishment candidate.
Allegations of vote-rigging in the original ballot were just part of a campaign characterised by alleged dirty tricks.
In a televised debate between the two rivals, which at times seemed to degenerate into a shouting match, Mr Yushchenko accused the government of "trying to steal Ukraine's future".
Doctors recently confirmed that Mr Yushchenko, who developed a disfiguring skin condition in September, had been poisoned with dioxin.
The opposition leader has suggested he was poisoned at a dinner with heads of the Ukrainian security service (SBU) - an allegation denied by the SBU.