The first results are expected later from Nigeria’s tightest election since the end of military rule in 1999.
However, following widespread delays and some attacks on polling stations on Saturday, voting has been postponed until Sunday in parts of the country.
In other areas, voting continued through the night.
Turnout appears to be high, especially among young people who make up about a third of the 87 million eligible voters.
This makes it the biggest democratic exercise in Africa.
The election has seen an unprecedented challenge to the two-party system that has dominated Nigeria for 24 years.
Peter Obi from the relatively unknown Labour Party, Bola Tinubu from the ruling All Progressives Congress (APC) and Atiku Abubakar of the main opposition Peoples Democratic Party (PDP) are all seen as potential winners. There are 15 other presidential candidates.
Saturday’s voting was marred by long delays at polling stations, as well as scattered reports of ballot-box snatching and attacks by armed men, especially in southern areas, where Mr Obi has his support base.
Dr Nkem Okoli was just about to vote in the Lekki district of the biggest city Lagos when masked men attacked the polling station.
“There was pandemonium. There were bottles flying everywhere,” she told the BBC. “They broke [the ballot box]. They stole the phones of the officials. Now we can’t vote.”
Voting was delayed until Sunday in several parts of the southern Bayelsa state.
Harrison Rosaline said she waited for five hours to vote on Saturday but no election officials turned up. But she returned, with her two-month old baby, and is delighted to have finally cast her ballot.
“I was motivated because I want a better Nigeria. I want this country to be good for everybody including my baby,” she told the BBC.
