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Kenyans are voting amid tight security in a re-run of the presidential election, which is being boycotted by the main opposition.
A teenage boy was shot by police and later died amid clashes in Kisumu, an opposition stronghold where some have blocked access to polling stations.
President Uhuru Kenyatta was declared the winner in an August vote, but it is being held again over "irregularities".
Turnout appears high in ruling party strongholds but lower elsewhere.
Mr Kenyatta is seeking a second term. Opposition leader Raila Odinga has pulled out of the contest.
The polls opened at 06:00 (03:00 GMT) with tens of thousands of police and other security staff deployed to protect voters and polling stations.
International observers have scaled down their missions for security reasons.
One voter in Nairobi's Mathare slum, taxi driver David Njeru, 26, told the AFP news agency: "It is my duty to vote. Last time the queue was all around the block and I waited six hours to vote, this time the people are few."
After casting his vote in the town of Gatundu, Mr Kenyatta urged people to cast their ballots so the country could move on.
"We're tired as a country of electioneering. It's time we moved forward," he said, adding that most of the country was "calm and peaceful".
What has happened since the first vote?
President Uhuru Kenyatta, posing here with a voter, said it was time for the country to move on
The announcement by the Independent Electoral and Boundaries Commission (IEBC) of Mr Kenyatta's victory on 8 August led to inflammatory rhetoric and attacks on the body.
Last week, a senior member of the IEBC fled to the US amid death threats.
About 50 people are reported to have been killed in violence since Mr Kenyatta was declared the winner in August's election.
Mr Odinga had wanted the repeat ballot to be held at a later date, but a bid to delay the election re-run fell apart after only two of seven Supreme Court judges attended a hearing on Wednesday.
One judge, Deputy Chief Justice Philomena Mwilu, failed to appear after her bodyguard was shot and wounded by unknown gunmen on Tuesday.
Why is there an election re-run?
Kenya's Supreme Court took the unprecedented decision to annul the August presidential election and demand a re-run in September citing "irregularities and illegalities".
Voting in the re-run has been calm in most areas
Chief Justice David Maraga said the election had not been "conducted in accordance with the constitution" and declared it "invalid, null and void".
He said the verdict, which was backed by four of the six Supreme Court judges, found that the IECB had committed irregularities "in the transmission of results".
The court said the result was "neither transparent nor verifiable".
The ruling did not attribute any blame to President Kenyatta's party or campaign but it nevertheless raised tensions, with rival protests in support of and against the court.
There were running battles between police firing tear gas and stone-throwing protesters in the city of Kisumu, an opposition stronghold, on Wednesday.
Why is the opposition boycotting?
Mr Odinga has said that the IECB failed to make the changes needed to prevent a repeat of the mistakes that marred the earlier poll, although the IECB disputes this.
His opposition coalition - the National Super Alliance (Nasa) - made clear its participation in the election was contingent on reforms being made.
Raila Odinga told his supporters: "We are going to win the battle"
Mr Odinga had vowed to disrupt Thursday's vote, calling for "massive" demonstrations, but has asked his supporters to stay away from polling stations in an attempt to avoid violent clashes.
In a statement earlier this month, he accused the government of instituting a "dictatorship", adding: "We are going to win the battle for a free and fair election".
"Our opponents want an election for the sake of it, we want a better election," he said.
(BBC)
