One exit poll by the Kyiv International Institute for Sociology, which sampled 460 polling stations across the country, gave Yushchenko 56 percent of the vote to Yanukovych's 41 percent. Another other poll, by the Socinform group, gave Yushchenko a bigger lead: 58 percent to Yanukovych's 38 percent.
First official results were not expected until today, but Yanukovych last night hinted that he might not win, vowing to "fight in opposition" if he loses.
Yushchenko supporters began gathering in central Kyiv.
New Political Landscape
The election has transformed the Ukrainian political landscape.
Fears the balloting process would be fraudulent sent hundreds of thousands of Yushchenko supporters into the streets in November. The "Orange Revolution," as the protest became known, led to the Supreme Court ruling and yesterday's new vote.
The election is also likely to determine Ukraine's main foreign policy orientation. Yushchenko advocates NATO and European Union membership for Ukraine and promised market and democratic reforms and to root out corruption.
Yanukovych, a supporter of close links with Russia, has been heavily backed by the Kremlin. He promised to make Russian a state language and offer dual Ukrainian-Russian citizenship if he won.
Reports from Ukraine said polling in general proceeded smoothly, with relatively few problems.
Voter Jan Yukhemovych emerging from a central Kyiv polling station yesterday, was optimistic the election would be honest.
"I have the feeling that, yes, today the elections will be much more honest than 21 November. Today we have a great hope that for the first time in our lives we will have a government that we can dream about," Yukhemovych said.
Hanna Husheryvna, a pensioner, said she voted for Yushchenko in each round: "Three times, three times I have voted for Yushchenko. I hope very much that he will be our president in an honest manner, because an honest person will be very good for our country."
The daughter of Ukraine’s national soccer coach, singer Iryna Blokhina, flew from her new home in California to vote for Yushchenko yesterday. She said the effort and cost was worth it if the country finally achieves democracy.
"I definitely voted for Yushchenko," Blokhina said. "I believe in a free country. It's a beautiful country. It’s got so much talent here, and it deserves the best because it produces so many beautiful [good] people and it gives so much to the world that it deserves some peace."
The manager of a Kyiv casino, Roman Dianov, said he voted for Prime Minister Yanukovych because he liked him more as a person than Yushchenko. Although he did not particularly dislike Yushchenko, he did not like the fact that his supporters had occupied the center of Kyiv for a month.
"I familiarized myself with Viktor Fedorovych [Yanukovych's] program, and it appealed to me," Dianov said. "He proposes stability for our society -- social as well as economic. In his manifesto he proposes two languages for Ukraine: Russian and Ukrainian. I also like that because in Ukraine much of the population speaks Russian."
Seemingly Smooth Polling
More than 300,000 Ukrainians were present as monitors at the country's 33,300 polling sites. More than 12,000 foreign observers were on hand to watch the election process.
While no major problems were reported, both sides traded accusations of minor violations. Yushchenko supporters said their opponents rigged voting at a few individual polling sites in the Kharkiv, Odesa, Zaporizhia, and Dnipropetrovsk region, chiefly by abusing home-voting rules for the handicapped and elderly.
Yanukovych supporters accused their opponents of turning off lifts in tall buildings in Kyiv and preventing invalids from being transported to polling sites, among other gambits, to prevent ballots being cast in favor of the prime minister.
ITAR-TASS said observers from the Commonwealth of Independent States registered several voting violations in western Ukraine.
But the charges seemed to pale in comparison with the large-scale fraud that occurred in November, when Yanukovych voters were bused to several polling stations to cast several ballots in one day and some regions reported 96 percent turnout for the government-backed candidate.
The chairman of Ukraine's revamped Central Election Committee, Yaroslav Davydovych, said his officials were checking into the allegations of vote fraud this time around. But he said he believed the vote had proceeded smoothly.
[For more RFE/RL coverage and analysis, see our dedicated "Ukraine's Disputed Election" website.]