Zimbabwe's electoral commission said on Tuesday there had been no vote-rigging in the first election without Robert Mugabe on the ballot, but the opposition alleged irregularities as an anxious nation awaited the first official results.Dozens of opposition supporters gathered at their headquarters in the capital, Harare, celebrating in the belief that they had won the presidential election based on results they said they collected from agents in the field. Police with water cannon circulated in the area.Zimbabweans hope the election will help to lift their country out of economic and political stagnation. Millions peacefully cast their ballots on Monday in a process closely watched by international monitors, who have yet to make formal announcements about whether the election was free and fair.* To follow the latest on the Zimbabwe elections SIGN UP TO THE HELLO AFRICA NEWSLETTERFOLLOW News24 Africa on Twitter and Facebook. The Zimbabwe Electoral Commission said the first results were expected on Tuesday afternoon, with the final tally expected within five days. The turnout varied from 60% to 78% with some areas still reporting."The atmosphere has remained peaceful" and the commission had not received any major complaints about how the election was conducted, chief Priscilla Chigumba told reporters.She said she was confident there was no "cheating" and that the commission will respect the will of Zimbabweans: "We will not steal their choice of leaders, we will not subvert their will."Hours after Chigumba spoke, the main opposition party, the Movement for Democratic Change, said voting results were not posted outside 21% of the country's nearly 11 000 polling stations as the law requires, raising concerns about possible vote-rigging.Opposition leader Nelson Chamisa, a 40-year-old lawyer and pastor, has said he would lead peaceful protests if the vote is found to be flawed.The other main contender is 75-year-old President Emmerson Mnangagwa, a former deputy president and Mugabe confidante who has reinvented himself as a candidate for change.Both candidates issued upbeat assessments of how they did, though said they were waiting for the electoral commission to make the final announcement as required by law."I am delighted by the high turnout and citizen engagement so far," Mnangagwa said on Twitter."We've done exceedingly well," Chamisa tweeted.If no presidential candidate wins more than 50% of the vote, a runoff will be held September 8.More than 5.5 million people were registered to vote in an election featuring a record number of more than 20 presidential candidates and nearly 130 political parties vying for parliamentary seats.The presence of Western election observers in Zimbabwe reflected a freer political environment since the November resignation of Mugabe, who had ruled since independence from white minority rule in 1980. Mugabe, forced out under military pressure, had declared he would not vote for the ruling party he long controlled and called Chamisa the only viable candidate.There remained concerns about bias in state media coverage of the election, a lack of transparency in ballot printing and reports of intimidation by pro-government local leaders who are supposed to stay neutral.Elmar Brok, head of the European Union monitoring mission, said his team had noted some "inconsistencies" but that overall there was progress compared to past elections. Under Mugabe, elections were often marred by violence, harassment and irregularities."In African elections, often stakes are very high and nobody has a backup plan for losing," said John Dramani Mahama, former president of Ghana and head of the observer mission from the Commonwealth group of nations, mostly former British colonies.The contenders in Zimbabwe's vote must accept the results and "should look at the larger picture of success, a successful election for Zimbabwe," he said.A voter in Harare said Zimbabwe is anxious to hear the election results as soon as possible."Because people are not yet settled, they're thinking of too many things," said 65-year-old Chaka Nyuka. "They need a good change. People are looking for that."