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The turnout appeared to be tremendous. Starting hours before dawn, lines of voters wrapped in blankets and heavy coats stretched for nearly a mile in some places.

Already, some violence has flared. In Mombasa, at least four police officers were butchered with machetes in an overnight attack that authorities believe was carried out by the Mombasa Republican Council, a fringe separatist group that opposes the elections and believes Kenya's coast should be a separate country. Some Western election observers in Mombasa, the biggest city on Kenya's Indian Ocean coast, have pulled back to their hotels because of security concerns.

In northeastern Kenya, near the border with Somalia, there was a small explosion at a polling station and a grenade was thrown into a police camp. Early reports indicated there were few, if any, casualties in the incidents.

Kenya's top politicians are urging voters to remain calm and avoid the mayhem that erupted at the end of 2007 and early 2008 when a disputed election ignited ethnic grievances and set off clashes that killed more than 1,000 people.

"We must keep the peace," said William Ruto, after voting Monday in his hometown, Eldoret. Mr. Ruto is running for deputy president and has been charged by the International Criminal Court with crimes against humanity connected to the violence in the last election.

Raila Odinga, Kenya's prime minister and one of the leading contenders for president, brimmed with confidence as he stepped into a cardboard ballot box in a Nairobi slum and cast his vote. "Today, Kenyans have a date with destiny," he said.

Kenya is one of the most industrialized countries in Africa, a beachhead for Western interests and a close American ally but its history has been haunted by intense and often violent ethnic politics. Mr. Odinga, an ethnic Luo, says he was cheated out of victory in 2007.

His main rival is Uhuru Kenyatta, a Kikuyu and the son of Kenya's first president. Mr. Kenyatta has also been charged by the International Criminal Court with crimes against humanity, accused of bankrolling Kikuyu death squads that murdered scores of Luo civilians in 2008. The Kikuyu-Luo political feud goes back decades to Kenya's independence in 1963.

Many analysts predicted that neither Mr. Odinga nor Mr. Kenyatta will win more than 50 percent of the vote, mandating a heated runoff in April.

The voting on Monday seemed to be proceeding smoothly in some areas but was bumpy in others, with polling stations not opening on time. There were also problems with the new biometric voter identification process. The new digital equipment was not working at many polling stations and officials had to revert to printed voting lists, which are thought to be more susceptible to corruption.

This election is the most complicated Kenya has ever held. A host of new positions have been created, like governorships, senate seats and county women's representatives, in an attempt to change the winner-take-all nature of Kenyan politics. In some places, the sheer number of ballots caused long delays.

"The cracks are beginning to show," Mr. Odinga said Monday morning. But he added he was still confident that, this time, he would win.