Zimbabwean election officials have been allowing people to vote after the official end of polling, as a high turnout led to long queues.
Most polling stations are now closed but a few have stayed open for late voters in the fiercely contested presidential and parliamentary poll.
President Robert Mugabe, 89, has said he will step down after 33 years in power if he and his Zanu-PF party lose.
PM Morgan Tsvangirai's MDC says Zanu-PF doctored the electoral roll.
It said the rolls contained the names of two million dead people, and there were concerns about the number of people being turned away from polling stations. Zanu-PF denies the claims.
Zanu-PF and the Movement for Democratic Change (MDC) have shared an uneasy coalition government since 2009 under a deal brokered to end the deadly violence that erupted after a disputed presidential poll the previous year.
Mr Mugabe dismissed the MDC's allegations of vote-rigging as "politicking" as he voted in the capital Harare's Highfield township.
"They want to find a way out," Mr Mugabe said.
"I am sure people will vote freely and fairly, there is no pressure being exerted on anyone."
Mr Tsvangirai described casting his ballot as an emotional moment "after all the conflict, the stalemate, the suspicion, the hostility".
"This is a very historic moment for us," he said.
Mr Tsvangirai won the most votes in the first round of the 2008 poll, but pulled out of the run-off with Mr Mugabe because of attacks on his supporters, which left about 200 dead.
The government barred Western observers from monitoring Wednesday's elections, but the African Union (AU) and the Southern African Development Community (Sadc), as well as local organisations, have been accredited.
Polls opened at 07:00 local time (05:00 GMT) and had been due to close at 19:00.
However, because of the high turnout election officials said people who were still waiting in queues to vote by 19:00 would have until midnight to cast their ballots.
Results are due within five days.
Zimbabwe Election Support Network, the main domestic monitoring agency, said the vote appeared to be taking place without too many problems, Reuters news agency reports.
"There are some concerns around long queues, but generally, it's smooth," said its spokesman Thabani Nyoni.
Former Nigerian President Olesegun Obasanjo, who heads a group of African Union monitors, said the elections seemed credible.
"It's been quiet, it's been orderly. The first place I called in this morning, they opened prompt at seven o'clock and there haven't been any serious incidents that... would not reflect the will of the people." he told Reuters.
Big queues have been reported across the country, but there have been numerous complaints that voters were unable to find their names on the electoral roll.
According to villagers, MDC polling agents and local election observers, some irregularities were recorded in parts of rural Masvingo district.
Traditional leaders and village heads are alleged to have lined up residents, forcibly marched them to the polling stations and given them voting numbers as if to cross-check who they had voted for.
There are also suggestions that in these rural areas some literate people were forced to pretend they could not read or write and were assisted to cast their vote in favour of Zanu-PF.
On Tuesday, the MDC accused Zanu-PF of doctoring the roll of registered voters, which was released by the Zimbabwe Electoral Commission (Zec) only on the eve of the polls after weeks of delay.
The MDC claimed the roll dated back to 1985 and was full of anomalies.
A BBC correspondent has seen the document and says it features the names of thousands of dead people.
MDC Secretary-General Tendai Biti said there were as many as two million such names, while some genuine voters were not finding their names on the rolls.
"The greatest worry which we have is the number of persons that are being turned away," he added.
A Zanu-PF spokesman denied the allegations and pointed out that appointees from both parties were on Zec. He also accused Mr Biti, who is Finance Minister, of not funding the commission properly. Zec has not commented.
In addition to Mr Mugabe and Mr Tsvangirai, there are three other candidates standing for the presidency - Welshman Ncube, leader of the breakaway MDC-Mutambara; Dumiso Dabengwa of the Zimbabwe African People's Union (Zapu), and Kisinoti Munodei Mukwazhe, who represents the small Zimbabwe Development Party (ZDP).
To be declared a winner, a presidential candidate must win more than 50% of the vote. If no candidate reaches this mark, a run-off will be held on 11 September.
The elections will be the first to be held under the new constitution approved in a referendum in March this year.