Bakiev came to office in March when crowds protesting controversial parliamentary elections overran the seat of government.
Exit polls taken by three Western-funded Kyrgyz pollsters give Bakiev over 80 percent of the vote. The closest of his five opponents, Akbaraly Aitikeev, got about 5 percent.
About 2.6 million voters were eligible to take part in the election, for which 2,000 polling stations were set up.
Full preliminary results, as well as a verdict on the fairness of the poll from the Organization for Security and Cooperation in Europe, are expected late tomorrow.
The Central Election Commission has said that today's presidential election is valid. According to the commission, around 53 percent of voters participated before 1700 Bishkek time (1300 Prague
time). According to the law, one vote over 50 percent is needed for the election to be deemed valid. Clear Frontrunner
There are six contenders but one candidate -- current acting President Kurmanbek Bakiev -- is the clear frontrunner. The drama today centers less on who will win the race than upon whether Kyrgyz voters turn out in large numbers and whether the vote will be perceived as free and fair.
Those conditions must be met if the new Kyrgyz government is to get the popular mandate it needs to bring stability to a country that has seen considerable unrest since former President Akaev was driven from power in street protests in March.
Voting officials have organized concerts in an effort to draw voters to the polls. But they are also trying to boost voter turnout in other ways.
One is by extending voting hours. The polls opened at seven in the morning local time, an hour earlier than in previous elections. And they won't close again till nine in the evening, an hour later than usual.
One voter who has already turned out early today is the frontrunner candidate -- acting President Kurmanbek Bakiev. Surrounded by journalists at a polling station in the Pervomai district in central Bishkek, he sought to ease concerns over voter turnout by predicting that it will be high.Strong Mandate
A high turnout is necessary for any new president to get the kind of strong popular mandate his government would need to bring political stability to Kyrgyzstan. The country has seen considerable unrest since former President Askar Akaev was ousted in street protests in March -- protests in which supporters of Bakiev and other opposition figures took part.
At the polling station, Bakiev also sought to assure the public that today's vote will be free and fair. That is the other condition that must be met if a newly elected president is to have the country's support.
"The uniqueness of these elections is that for the first time since we acquired independence, these elections are real elections in the true meaning of this word. It means that each citizen of Kyrgyzstan has a right to choose one candidate among those registered. A voter gives his right to the one he chooses. No one pressures anybody. No one threatens or advises anybody," Bakiev said.
To check the transparency and fairness of the voting process, over 1,000 observers are monitoring the polls. And some 300 foreign journalists have received accreditation to work in Kyrgyzstan during the election period.
Some of the observers who are monitoring the polls told RFE/RL today that no violations have come to their attention so far. Bermet Abdyshukurova from Kyrgyzstan's largest civic group, the "Coalition for Democracy and Civil Society," said the vote was going well.
Most voters RFE/RL spoke to today as they exited polling stations said they had voted for Bakiev. Many of them said that to them Bakiev represents stability.
Many international and local groups have organized their own exit polls and the public comparison of their results will do a lot to confirm -- or contradict -- the official vote results.See also:
RFE/RL Special: Kyrgyz Presidential Election
Will Election Be Free, Fair, And Nonviolent?
Young Voters Have Their Say