Election officials have started to count the votes in Guinea-Bissau, after polls intended to restore stability to the impoverished, coup-prone state.
Final results are not expected for 10 days
Officials say the turnout was high, possibly more than the 75% who voted in last year's parliamentary polls.
Among the 13 candidates are two former presidents, including Kumba Yala, who was deposed in a bloodless coup in September 2003.
Long lines formed in many polling stations in the capital, Bissau.
"All we're hoping for is peace - that's the most important thing," said Celestina Sanca, a 37-year-old market seller with eight children.
Sunday's vote aims to build on the March 2004 parliamentary elections, which were praised as "free, fair and transparent".
The three main candidates are Mr Yala, Joao Bernardo "Nino" Vieira, also a former president, and Malam Bacai Sanha of the African Party for the Independence of Guinea and Cape Verde (PAIGC), which led the 1970s guerrilla war to oust colonial Portugal.
Both Mr Yala, who still considers himself as the legal head of state, and Mr Vieira, who ruled the country for almost 19 years, were allowed to stand in the election after being previously barred.
Kumba Yala PRS. Support base: Balanta ethnic group
Nino Vieira Independent. Support base: Urban youth
Malam Bacai Sanha PAIGC. Support base: Veterans of 1970s war of independence
While it is hoped that the new leader will turn the country's fortunes around, some fear that the losers may not accept the results, plunging Guinea-Bissau into a new round of conflict.
Final results are not expected for 10 days.
Decades of instability have made Guinea-Bissau one of the world's poorest countries.
According to the UN, 80% of its population lives on less than $2 (£1.60) a day.
The next leader of this former Portuguese colony of 1.4 million people will have to find a way of reviving the sluggish economy centred on cashew-nut production.
The vote is being monitored by some 200 observers from the US, the EU and west African states.