Mugabe, 84, of the ruling Zanu-PF party, faces two major opponents: leading opposition figure Morgan Tsvangirai and Mugabe's former finance minister, Simba Makoni, both supported by different factions of the Movement for Democratic Change, the main opposition party.

Critics have predicted the elections will be marred by fraud, though the government has promised they will be "free and fair."

The Zimbabwean government has denied CNN and other international news organizations permission to enter the country to report on the elections, but Zimbabweans crossing the border into South Africa on Saturday told CNN there was good voter turnout with long lines at polling stations, and a heavy police and army presence. Read about reporting on the elections.

But less than an hour after voting began at 7 a.m. (1 a.m. ET), both opposition factions said that in at least 19 polling stations, the Zimbabwe Electoral Commission claimed to have "lost" the accreditation for the opposition's polling agent, so it refused to let the agent in.

Eddie Matsangaise of the Zimbabwe Exile Forum said he had heard reports that the names of long-dead white colonialist leaders were on voter lists, but voters who thought they were registered were turned away.

"Obviously they're not free and fair," Matsangaise said of the elections.

Voter confusion is a problem. The elections are not just for president, but also for parliamentary, senate, and local council seats, meaning voters have to cast a number of ballots in a limited amount of time.

Limited voter education means many registered voters were not told which ward to go to and may turn up to the wrong polling station. In heavily-populated urban areas -- traditionally opposition strongholds -- Zimbabweans said there were too few polling stations.

Mugabe's critics say a recent move by Mugabe to increase the salaries of the police, army, and teachers and hand out machinery to black farmers was a vote-buying move. The government denies it was linked to the vote.

The absence of international media and independent observers has heightened critics' concerns. The United States this week warned of a possible unfair election, and New York-based Human Rights Watch warned earlier this month that the elections were likely to be "deeply flawed."

Human Rights Watch said in a report that Zimbabwe's electoral commission is partisan toward Zanu-PF and lacks both expertise and resources to run the elections properly.

An MDC official this week said leaked correspondence from the electoral commission showed it had asked for 3.3 million more ballots than there are registered voters -- including 250,000 extra postal ballots for soldiers and police. Tenda Biti, MDC secretary-general, said it was an indication of fraud. Voting was scheduled to close at 7 p.m. (1 p.m. ET).

Of the three candidates standing against Mugabe, Tsvangirai and Makoni have good chances of winning.

Tsvangirai founded the MDC and led hotly contested challenges against Mugabe in 2000, 2002, and 2005.

Makoni used to be a member of the Zanu-PF and served as the country's finance minister, but the party expelled him after he announced his bid to unseat Mugabe.

A hero of the country's civil war against the white Rhodesian government, Mugabe became the country's first black prime minister in 1980. But nearly three decades later, he has consolidated his rule over all aspects of Zimbabwean life, and the country does not appear better for it.

His country was once revered for offering its citizens some of the best education and health care in Africa, but now schooling is a luxury and Zimbabwe has one of the lowest life expectancies in the world.

Zimbabwe was once known as the breadbasket of southern Africa, but now it's difficult to get even basic food supplies. Inflation has skyrocketed to more than 100,000 percent while food production and agricultural exports have dropped drastically.

Thousands of Zimbabweans flood into neighboring countries looking for jobs.

Part of the economic freefall is traced to Mugabe's land redistribution policies, including his controversial seizure of commercially white-owned farms in 2000. Mugabe gave the land to black Zimbabweans he said were cheated under colonialist rule, and white farmers who resisted were jailed.

In 2005, Mugabe launched Operation Clean Out the Trash, in which he razed slum areas across the country.

Mugabe denies mismanagement and blames his country's woes on the West, saying sanctions have harmed the economy.