Sally Nabil reports from inside a polling station in Alexandria. Photo: BBC

A huge security operation has been mounted by police and the military, amid fear of attacks by militants seeking to disrupt the polls.

Former army chief Abdul Fattah al-Sisi, who deposed Islamist President Mohammed Morsi last year, is standing against left-wing candidate Hamdeen Sabahi.

Mr Sisi is forecast to win by a comfortable margin.

The elections are being held across two days, with unofficial results expected hours after polls close.

Shaimaa Khalil, BBC News, Cairo

There is a very festive atmosphere in central Cairo - more of a party than a poll. Posters of Abdul Fattah al-Sisi and Egyptian flags are the accessories of the day.

"Sisi is Abdel Nasser!" said one elderly woman, referring to the popular late president, who was also a military man. "He'll bring back our Egypt," she added. "Tell them. Let the whole world know."

Perception is everything in this election. This is not about who will win - the former defence minister is the clear front-runner. This is about how big the turn out will be and how big his mandate is. Even his only rival, Hamdeen Sabahi will tell you his chances of winning are next to none.

The spirits are high but so are the stakes. Whoever ends up in the presidential palace will have to deliver on the two crucial things that have crippled Egypt so far - security and the economy.

The massive security operation is not just to keep voters safe - it is also a message to Egyptians and the world and the security forces are back on the streets and in control.

Shortly after polls opened, Mr Sisi cast his vote at a polling station in Heliopolis, Cairo, amid a throng of reporters and spectators.

"The Egyptians are coming out to write their history and chart their future," said the 59-year-old, dressed in a dark suit and tie.

Mr Sisi appeals to Egyptians who crave stability after years of political upheaval and anything else than an easy win for him would be a source of astonishment, says the BBC's Kevin Connolly in Cairo.

The scale of turnout will be seen as an indication of the strength of endorsement of the winning candidate.

In Cairo, voters were queuing to cast their ballots almost an hour before polling stations opened, as military helicopters hovered overhead.

"We want security first, then everything else will follow," Manal Mohammed, a voter in the district of Imbabah, told the Associated Press.

More than 250,000 members of the security forces are on duty at polling stations across the country, according to the interior ministry.

The tight security drums home a familiar message from the military-backed interim authorities - that the dangers of Islamist militants are ever present, our correspondent says.

Abdul Fattah al-Sisi, one of two candidates, is expected to easily win

Hamdeen Sabahi is the only other candidate standing against Mr Sisi

Egyptians in Cairo queued to vote from early morning

Security is tight across the country, with the threat of attacks by militants

Egypt's interim authorities have clamped down hard on Mr Morsi's Islamist movement, the Muslim Brotherhood, declaring it a terrorist organisation.

More than 1,400 people have been killed and at least 16,000 arrested, including the Brotherhood's senior leaders.

President Morsi, who was deposed last July following mass protests, is standing trial on a raft of charges. He strongly denies any wrongdoing.

Islamists and some secular activists are boycotting the polls in protest at the clampdown and repression of dissent.

In his election campaign, Mr Sisi set out plans to develop agriculture, housing, education, impoverished areas and employment.

He is backed by several big businessmen as well as a broad range of political parties from the Islamist right to the moderate left.

Hamdeen Sabahi, who came third in presidential elections in 2012, offers an alternative to young voters who favour a civilian candidate over a former military one.

He promises to combat corruption and incompetence while promoting civil rights.

Both candidates say they will not re-legalise the Muslim Brotherhood.