Voters in Guinea are electing a president in the west African country's second democratic presidential election since independence in 1958.
Seven candidates are competing against President Alpha Conde, who is hoping to win a second term.
His main challenger, Cellou Dalein Diallo, has urged his supporters to vote despite the country's top court rejecting his plea for a delay.
The 2010 election saw a transition from military to civilian rule.
Since then Guinea has been badly hit by an Ebola outbreak and seen prices of key export bauxite - the raw material in aluminium - slump.
Deep ethnic, political and religious tensions persist and can quickly become violent, especially around election time, BBC World Service Africa editor Mary Harper reports.
At least three people were killed in pre-election violence.
Opposition parties had wanted the vote postponed due to alleged anomalies in the country's electoral roll but the election commission rejected the call.
Some of those trying to vote early on Sunday complained that voting materials were not ready.
Mr Conde is favourite to win the election but a second round of voting is likely.
"I ask all Guineans, whatever their party, to fulfil their civic duty peacefully and calmly," Mr Conde said after casting his vote in the capital, Conakry.
Aged 77, he is hoping to capitalise on his victory in the 2010 vote, held after he returned from some three decades in exile, but that election was marred by violence and accusations of fraud.
He promises to consolidate stability and social unity, and promote development.
After voting elsewhere in the capital, Mr Diallo, a former prime minister, said: "We must hope there will not be [violence] after the elections and that the people of Guinea show maturity."
The 63-year-old pledges to prioritise jobs for young people and to give all Guineans "access to health care, decent housing, water, electricity, safety, and justice".
African Union and European Union observers are monitoring the election. The official result is not expected until Monday or Tuesday.