Kenyans are voting in the first presidential polls since a new constitution came into force, designed to avoid the deadly tribal violence that erupted after polls five years ago.
It is the first time a vote has taken place under a new constitution, designed to prevent a repeat of violence that followed the 2007 polls.
More than 1000 people died in widespread ethnic violence when supporters of rival candidates clashed in 2008.
Despite appeals for calm, at least four police officers died after being attacked near Mombasa on Monday, the BBC reports.
At least six other people - including several attackers - are also reported to have died in the assault in the early hours in Changamwe, half an hour's drive from the centre of Mombasa.
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 last time.
Kenyans will choose a president, members of parliament and senators, county governors and members of 47 county assemblies. However, all eyes are on the presidency.
Eight candidates are standing, but it is essentially a two-horse race pitting Prime Minister Raila Odinga against Deputy Prime Minister Uhuru Kenyatta, the BBC reports.
If neither of the frontrunners poll more than 50% the vote will go to a run-off, probably on 11 April.
