With no reliable opinion polls, no one knows who will win the presidency but Egyptians enjoyed the uncertainty after the routinely rigged votes of Mubarak's 30 years in power.

"We must prove that the times when we stayed at home and someone would choose for us are over," said Islam Mohamed, a 27-year-old swimming coach, waiting at a Cairo polling station.

The election is a momentous sequel to Mubarak's overthrow on February 11 last year. The military council in charge of a messy and often bloody political transition since then has overseen a constitutional referendum, parliamentary polls and now a vote for a president to whom it has promised to hand power by July 1.

The revolutionaries of Tahrir Square might be reluctant to trust Egypt's future to Islamists or Mubarak-era politicians, but those candidates might appeal to many of the 50million eligible voters who yearn for Islamic-tinged reform or a firm and experienced hand to restore stability and security.

Whoever wins faces a huge task to relieve a dire economic outlook and will have to deal with a military establishment keen to preserve its privileges and political influence.

The relative powers of the president, government, parliament, judiciary and military have yet to be defined as the tussle about who should write a new constitution goes on.

"I will vote today, no matter what; it is a historic thing to do, though I don't really know who I will vote for," said Mahmoud Morsy, 23.

He then said he would probably plump for Mohamed Mursi, candidate of the Muslim Brotherhood, whose voting machine has already ensured it the biggest bloc in parliament.

The nation of 82million was in festive and relaxed mood, with many voters joking and chatting on a day to remember.

"Rise up Egypt" read a giant headline in the popular daily Al-Masry al-Youm, and state-run Al-Gomhuria offered: "The president is in the ballot box, the key is with the people."

Voters shuffled slowly towards the ballot booths in bright sunshine. Some had brought chairs and newspapers, expecting long lines, but turnout did not seem as high as in the winter vote for parliament, Egypt's first free election.

Egyptians also enjoyed seeing presidential hopefuls queuing alongside them to vote, in scenes a world away from past elections when state TV filmed a cosseted Mubarak casting his ballot among doting officials with no ordinary voters in sight.

In one Cairo district, Amr Moussa, 75, a former foreign minister and Arab League secretary-general, stood in line with everyone else.

"I hope they will elect a president who can really lead Egypt at this time of crisis," he said.

Some voters applauded independent Islamist contender Abdel Moneim Abol Fotouh, 60, when he joined a queue in Cairo.

"For the first time the Egyptian people went out to choose their president after the end of an era of 'pharaohs'," Abol Fotouh said.

Unless one candidate gets more than half the votes needed to win outright, the top two will face a run-off on June 16 and 17.