Egyptians queued patiently to vote yesterday, eager to pick their leader for the first time in a national history dating to the pharaohs, with Islamists and secular-minded rivals who served under deposed President Hosni Mubarak heading the field.

With no reliable opinion polls, no-one can accurately predict who will win the presidency, but Egyptians revelled in 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. There were no early reports of vote-related violence.

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The election is a momentous sequel to the popular revolt that toppled Mubarak 15 months ago. The military council in charge of a messy 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 may be reluctant to trust Egypt's future to Islamists or Mubarak-era politicians, but those candidates may appeal to many of the 50 million voters who yearn for Islamic-tinged reform or who want a firm and experienced hand to restore stability.

Whoever wins faces a huge task to relieve a dire economic outlook and will also 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 a tussle over who should write a new constitution rumbles on.

Many Egyptians were still undecided even as they went to the polls on the first of two days of voting. "I will vote today, no matter what. It is a historic thing to do, although 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 82 million was in festive and relaxed mood, with many voters joking and chatting on a day to remember.

"Rise up Egypt," ran a giant headline in the popular daily Al Masry Al Youm, while 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 and enjoyed seeing presidential hopefuls queueing beside them to vote. In one Cairo district, 75-year-old Amr Moussa, a former foreign minister and Arab League secretary-general, stood in a queue with everyone else. "I hope they will elect a president who can really lead Egypt at this time of crisis," he said.

One Moussa supporter, who gave his name only as Ahmed, relished the sight.

"Honestly, I like the idea of standing in line with the next president," he said.

Elsewhere in Cairo, some voters clapped independent Islamist candidate Abdel Moneim Abol Fotouh, 60, when he too lined up. "For the first time the Egyptian people went out to choose their president after the end of an era of 'pharaohs'," Mr Abol Fotouh said, alluding to Mubarak and his autocratic predecessors who, like him, were drawn from the top ranks of the military.

After the forged elections of the Mubarak era, voters were on alert for abuses.

In one Cairo polling station, a judge intervened after voters complained that an election official was promoting an Islamist candidate. Most voting was going smoothly.

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. Official first-round results will only be announced on Tuesday, but the outcome could be clear by Saturday.

l A policeman in a patrol car parked outside a polling centre in northern Cairo was killed by a stray bullet when a nearby argument over a taxi fare turned into a gun fight, according to security officials.