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People have been forming long queues at one polling station in Harare, as Nomsa Maseko reports.
Long queues have formed at polling stations in Zimbabwe as people vote in fiercely contested elections which have already been hit by fraud allegations.
President Robert Mugabe, 89, has said he will step down after 33 years in power if he and his Zanu-PF party lose.
Prime Minister Morgan Tsvangirai's Movement for Democratic Change (MDC) have accused Zanu-PF of doctoring the electoral roll, a charge it has denied.
Campaigning for the presidential and parliamentary poll was mostly peaceful.
Zanu-PF and the 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.
'Determined to vote'Mr Mugabe dismissed the MDC's allegations of vote-rigging as "politicking" as he voted in the capital Harare's Highfield township, AFP news agency reports.
At the scene
Thabo Kunene Bulawyo
Hundreds braved the cold and the wind to stand in queues, which started forming as early as 04:30 (02:30 GMT). A security guard said he saw some people sleeping opposite one polling station. Women selling tea and coffee nearby made good business as those in the queues dashed to buy the hot drinks to ward off the cold.
At one polling station in Makhokhoba, voting was progressing in an impressively ordered manner. People from different parties were chatting to each other and laughing but they avoided discussing who would win.
However some voters were disappointed after they failed to find their names in the wards where they had registered, raising more fears of vote rigging. After voting, some complained that the photos of the candidates were blurred and they had difficulties recognising them on the ballot papers.
Far away from the voting booth, Mlungisi Sibanda told me he woke up at 04:00, bathed and prayed before joining his friends in the queue. "If we don't make history in this election, we will never do it again," he said.
"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 is quoted by AFP as saying.
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 has 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 are due to close at 17:00 GMT.
The turnout is expected to be high among the 6.4 million people registered to vote, with tens of thousands attending rallies in recent weeks. Results are due within five days.
Wednesday has been declared a national holiday to ensure people can vote. Despite this, voters queued for several hours outside polling stations before they opened, reports the BBC's Nomsa Maseko in Harare.
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.
Continue reading the main story"I got up at four but still couldn't get the first position in the line," Clifford Chasakara, a voter in the western province of Manicaland, told the Reuters.
"My fingers are numb, but I'm sure I can mark the ballot all the same. I'm determined to vote and have my vote counted."
At a news conference at State House on Tuesday, Mr Mugabe was asked if he and Zanu-PF would accept defeat.
"If you go into a process and join a competition where there are only two outcomes, win or lose, you can't be both. You either win or lose. If you lose, you must surrender," he said.
'Anomalies'Zimbabwe election: Key facts
- About 6.4 million registered voters
- Polls open at 05:00 GMT and close at 17:00 GMT
- Vote for president and parliament
- Zanu-PF's Robert Mugabe and MDC's Morgan Tsvangirai are the main presidential contenders
- Mr Mugabe, 89, is seeking to extend his 33-year rule
- Mr Tsvangirai, 61, hopes to become president after three failed attempts
- The poll ends the fractious coalition between Zanu-PF and MDC, which was brokered by regional mediators after disputed elections in 2008 that were marred by violence
- First election under new constitution
But Mr Tsvangirai dismissed the president's remarks.
"He does not believe in the right of the people to choose. He does not believe he can be voted out of office," he told the BBC.
The 61-year-old has vowed to push Mr Mugabe into retirement; it is his third attempt to unseat him.
An MDC spokesman said separately that the party was only prepared to accept the results of the elections if they were "free and fair".
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. He says many names with the same address appear two or three times.
A Zanu-PF spokesman denied the allegations and pointed out that appointees from both parties were on Zec. He also accused Finance Minister Tendai Biti, from the MDC, 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.
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