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The BBC's Gabriel Gatehouse reports from a polling station in a Nairobi slum where violent clashes erupted in 2007
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Mapping the divides
Votes are being counted in Kenya after an election that observers describe as the most important in the country's history.
Polls were due to close at 17:00 (14:00 GMT) but officials said those in queues at that time would be allowed to vote.
Earlier there was violence near the port town of Mombasa, with at least five policemen killed in one attack.
Provisional results suggested the two main presidential candidates were far ahead of the rest of the field.
Partial preliminary results from areas where polling ended on time gave Uhuru Kenyatta a lead over Prime Minister Raila Odinga, although analysts cautioned that these results came from Kenyatta strongholds.
The two front-runners were well ahead of the other presidential candidates.
Mr Kenyatta is due to face trial at the International Criminal Court (ICC) next month in connection with the widespread bloodshed that followed the disputed 2007 election - he denies organising attacks.
Mr Odinga says he was cheated of victory last time.Biometric kits fail
Kenyans are choosing a president, members of parliament and senators, county governors and members of 47 county assemblies.
All eyes are on the presidency: Eight candidates are standing but it is essentially a two-horse race pitting Mr Odinga against Mr Kenyatta, analysts say.
Continue reading the main story
At the scene
Wanyama ChebusiriBBC News, Eldoret
At a polling station close to the church where more than 40 people who had sought shelter there on 1 January 2008 were burnt alive most voters were happy to have cast their ballots in peace. "This vote is a new beginning," said a man who lost relatives in the fire.
Gabriel GatehouseBBC News, Nairobi
The queues in some places stretched for more than a kilometre, as voters in Kibera slum stood patiently in line. As the sun grew hotter and the umbrellas came out, the mood was upbeat. "Peace, peace," one crowd shouted as a truck of paramilitary police trundled past.
Kenya: Vote around the country
Some observers say they are particularly concerned about violence erupting should neither of the two front-runners poll more than 50% - in which case the vote will go to a run-off, probably on 11 April.
Authorities had urged Kenyans to avoid a repeat of the 2007 ethnic and political violence that killed more than 1,000 people amid claims the poll had been rigged.
As thousands continued to queue to cast their ballots, voting was extended by up to seven hours to cope with long queues at polling stations.
Kenya's Independent Electoral and Boundaries Commission (IEBC) issued a notice via social media saying: "We wish to inform members of the public that all Voters on the queue by 5:00pm will be allowed to vote."
The electoral commission said some delays were caused by a new system intended to reduce fraud, which observers hope will prevent the kind of widespread ethnic violence that followed the last poll in 2007.
After he cast his ballot, Mr Odinga said he would accept defeat - but added that he was confident of victory in the first round.
"I will congratulate the winner," he said.
Mr Kenyatta also sounded a conciliatory note, saying the president would represent the whole country and that any disputes should be taken to court.
Reports from around the country suggested long queues of voters had formed even before polling stations opened - and some voters, such as those in Eldoret, were waiting up to 10 hours to cast their ballots.
Some technical difficulties were reported with newly instituted biometric voting kits - designed to counter claims of vote-rigging and long delays in announcing poll results that were partly blamed for the violence in 2007.
In places, electoral officials had to use the manual voter registers, delaying voting. But Lilian Mahiri-Zaja, vice-chair of Kenya's independent electoral commission, said the registers were complete and there was no reason why the election should not be credible.
These people were queuing outside St Mary's polling station in Nairobi
Five police officers and at least six other people - including several attackers - died in the assault in the early hours in Changamwe, half an hour's drive inland from the centre of Mombasa.
There have been further disturbances in the town of Kilifi, north of Mombasa, where six civilians were killed, but details of the incident remain sketchy.
Police pointed the finger at Kenya's coastal separatist group, the Mombasa Republican Council (MRC), but it denied responsibility, saying the group only sought change through peaceful means.
In other developments:
The BBC's Bashkas Jugsodaay in Garissa says there were three explosions in three different polling stations in Mandera, a town near the border with Somalia, as officials were preparing for polls to open. One person died, reports said
As well as the two deadly attacks near Mombasa, a third attack was reported in a village near Mishomoroni, but there was no information about casualties
In Kiharu, Muranga county, a 72-year-old woman fainted and died while waiting to cast her vote
It was unclear whether the deaths around Mombasa were election-related, but the Kenyan police chief said one of the attacks involved over 200 gang members, and in response he was sending an additional 400 officers to the area.Near-impunity
Waiting in line outside polling stations in Nairobi hours before polls opened, the atmosphere was calm and people chanted "peace", reports the BBC's Gabriel Gatehouse.
Raila Odinga vs Uhuru Kenyatta
Son of Kenya's first president, Jomo Kenyatta
Due to stand trial at ICC in April accused of organising violence in last election
His running mate, William Ruto, also accused
Both deny the charges
From Kikuyu ethnic group - Kenya's largest at 22% of population and powerful economically
Kikuyus and Ruto's Kalenjin community saw fierce clashes after 2007 poll
Currently deputy prime minister
Raila Odinga son of first Vice-President Jaramogi Oginga Odinga
Distant relative of Barack Obama
Believes he was cheated of victory in last election
From Luo community in western Kenya - 11% of population.
Some Luos feel they have been marginalised by central government
Third time running for president
Currently prime minister under power-sharing deal to end violence last time
Profile: Uhuru Kenyatta
Profile: Raila Odinga
In Garissa, frustration grew in the long queues as the heat beat down, our correspondent reports. Some used umbrellas to shelter from the sun and others bought water to pour over their heads.
Mr Kenyatta, son of Kenya's founding father Jomo Kenyatta, is due to stand trial at the ICC in April for his alleged role in orchestrating the violence five years ago.
Mr Kenyatta's running mate, William Ruto, has also been indicted. Both men deny any wrongdoing.
The 2007 violence broke out after Mr Odinga claimed he had been cheated of victory by supporters of President Mwai Kibaki.
Supporters of the rival candidates, from different ethnic groups, took up arms against each other. Mr Odinga later joined a government of national unity under a peace deal.
The underlying sources of tension in the 2007-8 election remain, and in some parts have escalated, with the risk of violence "perilously high", warns Human Rights Watch.
It says the "near total impunity" of the perpetrators of violence has left them free to rape and kill again.
Some 99,000 police officers have been deployed around the country.
Presidential candidates must secure support from across the country to be declared the winner, so they cannot just rely on support from their ethnic groups, as has been the case in previous elections.
Official results will be announced by 11 March by the electoral commission.