Egyptians are voting for a second and final day to elect the country's first president since Hosni Mubarak was forced from office in 2011.
Islamist Mohammed Mursi is up against former Mubarak Prime Minister Ahmed Shafiq in a second-round run-off.
The vote also comes amid a bitter row over the dissolution of parliament following a court ruling on Thursday.
Mr Mursi's Muslim Brotherhood has denounced the step as unlawful and a coup against democracy.
The movement urged Egyptians to protect their revolution after the ruling Supreme Council of Armed Forces (Scaf) declared the parliament null and void on Saturday.
Two days earlier, the Supreme Constitutional Court ruled that last year's legislative polls were unconstitutional, in a decision made by judges appointed under Mr Mubarak.
The dispute has laid bare the fears of some that the military council is trying to consolidate power and resist the democratic changes demanded during last year's demonstrations.
Soldiers have already been stationed around the parliament with orders not to let MPs enter.
Pro-revolutionary groups meanwhile say they will stage a protest in Cairo's Tahrir Square on Sunday night to keep up the pressure for reforms.
Law and order
The BBC's Jon Leyne says that there is less enthusiasm in the run-off election than there was for previous rounds of voting, and some have called for a boycott or spoiled ballots.
Many voters have expressed scepticism at the choices they face, and have voted with reluctance.
"Boycotting the elections is not a practical solution because at this point one of the two candidates will win anyway," Saber Abdullah, voting in Alexandria, told the BBC.
"I demand the next president to concentrate on helping the youth because the old regime have ignored them to the extent that they have reached rock bottom."
Mr Shafiq has campaigned on a platform of a return to stability and law-and-order which, correspondents say, many find attractive after months of political turmoil.
But to his critics, the former air force officer is the army's unofficial candidate and a symbol of the autocratic days under Mubarak.
Mr Mursi, meanwhile, has cast himself as a revolutionary and part of the movement that overthrew Mubarak, and has promised economic and political reform.
He has also softened his religious stance in an attempt to attract liberals and minorities.
His Freedom and Justice Party won almost half of seats in the legislature in the 2011 polls.
Mr Shafiq came second in last month's first round, in which turnout among the 52 million eligible voters was only 46%. Official results gave Mr Mursi 24.8% and Mr Shafiq 23.7%.
Final results from the Higher Presidential Election Commission (HPEC) are due by 21 June, but are expected to arrive much earlier.
PRI The World correspondent Matthew Bell, in the Nile Delta governorate of Sharqiya - birthplace of both candidates - says quality of life issues are of prime importance to voters there.
It is a rural and socially conservative area, where most voters chose the Muslim Brotherhood's candidate last year to represent them in parliament. It surprised analysts when Sharqiya produced a narrow win for Mr Shafiq in the first round of voting for president.
Manal Abdou, a child psychologist, said she decided to vote for Mr Mursi only a few days ago. She voted for another Islamist candidate - Abdel Moniem Aboul Fotouh - in the first round. "My priority is that the next president should have leadership skills and a national project that unites Egyptian youth and brings a rennaissance to Egypt," she said.
Ibrahim Abdel Moneim, a 67-year-old retired high school teacher had a different reasoning. "Ahmed Shafiq will save the country. We don't trust these people with beards," he said, adding, "if we don't like him, we can go back to Tahrir Square."
The vote comes at a time of growing political uncertainty in Egypt.
On Saturday, the top official in parliament, Sami Mahran, said he had received a letter from the Scaf confirming for the first time that the lower house, the People's Assembly, had been dissolved.
In response, the Muslim Brotherhood said the move was a "coup against the whole democratic process".
"The [March 2011] constitutional declaration does not give the Scaf such right," it said in a statement.
"The Scaf is hijacking the legislative authority in addition to the executive authority which Scaf is supposed to hand over within two weeks to a civilian authority."
The move followed Thursday's Supreme Court ruling that the law governing Egypt's first democratic elections in more than six decades was unconstitutional because party members were allowed to contest seats in the lower house reserved for independents.
Scaf officials have told state media that it now plans to issue a new interim constitution and potentially select a replacement constitutional panel itself.
The ruling Supreme Council of the Armed Forces (Scaf) has vowed to hand over power to the winner by 30 June.
But the decision to dissolve parliament so swiftly means that the new president could take office without the oversight of a sitting parliament and without a permanent constitution to define his powers or duties.