Polling stations have closed on the first of two days of Egypt's first free presidential election, 15 months after Hosni Mubarak was ousted.
Fifty million people are eligible to vote, and large queues formed at some polling stations.
The military council which assumed presidential power in February 2011 has promised a fair vote and civilian rule.
The election pits Islamists against secularists, and revolutionaries against Mubarak-era ministers.
But the BBC's Wyre Davies, in the second city of Alexandria, says that for many people the election is not about religious dogma or party politics, but about who can put food on the table.
The frontrunners are:
- Ahmed Shafiq, a former commander of the air force and briefly prime minister during February 2011 protests
- Amr Moussa, who has served as foreign minister and head of the Arab League
- Mohammed Mursi, who heads Muslim Brotherhood's Freedom and Justice Party
- Abdul Moneim Aboul Fotouh, an independent Islamist candidate
Until a new constitution is approved it is unclear what powers the president will have, prompting fears of friction with a military which seems determined to retain its powerful position.
Voting began at 08:00 (06:00 GMT), and throughout Wednesday long lines of voters were seen outside polling stations around the country.
Polling hours were extended to cater for the queues and frustrated voters were seen banging on polling station doors which were closed at 21:30. Voting will resume for a second day on Thursday at 08:00.
The interior ministry estimated turnout at less than 25% in some areas, and around 40% on others.
Proceedings were largely peaceful on Wednesday, with the health ministry reporting just 13 injuries across the country, due to overcrowding at polling stations and high temperatures.
NGOs and rights groups monitoring the elction reported some complaints.
Egypt's National Council for Human Rights (NCHR), an organization aimed at promoting human rights in Egypt, told the BBC they received 50 complaints on electoral violations ranging from delay in opening voing booths, to campaigning for candidates outside polling stations during voting.
There was a heavy police and military presence outside the 13,000 polling sub-stations and BBC correspondents said the atmosphere was mostly calm, with people waiting patiently for their turn to vote.
One police sergeant died after being shot during clashes between rival supporters in Rawdh al-Faraj on Tuesday evening, officials said.
"It's a very big day," one woman told the BBC earlier. "This is a real great moment for the Egyptians to change."
Another, when asked how long she had been waiting to vote, replied, with a laugh: "Thirty years."
Mr Mursi was originally the Muslim Brotherhood's reserve candidate, but he was thrust into the limelight after its first choice, Khairat al-Shater, was disqualified by the Higher Presidential Electoral Commission (HPEC) over an unresolved conviction.
He told reporters: "Today the world is witnessing the birth of a new Egypt. I am proud and cherish my membership of this people. I assure them that tomorrow will be better than today and better than yesterday."
Rash of crime
A run-off vote is scheduled for 16 and 17 June if there is no outright winner.
The election is being hailed as a landmark for Egyptians, who have the opportunity to choose their leader for the first time in the country's 5,000-year recorded history.
The Supreme Council of the Armed Forces (Scaf), worried about potential post-election unrest, has sought to reassure Egyptians that it will be the voters themselves who decide who will be the next president.
Its leader, Field Marshal Muhammad Hussein Tantawi, observed the election process at a number of polling stations.
The 15 months since Mr Mubarak was forced from power have been turbulent, with continued violent protests and a deteriorating economy.
Foreign direct investment has reversed from $6.4bn (£4bn) flowing into the country in 2010 to $500m leaving it last year.
Tourism, a major revenue generator for Egypt, has also dropped by a third.
The new president will have to reform the police to deal with the rash of crime that followed the uprising.
As many as a third of voters are reported to be undecided about which candidate to choose.
The Arab Spring began in Tunisia last year when weeks of protests forced President Zine al-Abidine Ben Ali from power, inspiring pro-democracy activists across the Arab world.
Mr Mubarak, who was in power for three decades, resigned on 11 February 2011 after 18 days of protests in Cairo and other cities.
He is on trial for his alleged role in the deaths of protesters, and a verdict in the case is due on 2 June.