Egyptians must decide between Ahmed Shafik, the last prime minister of Hosni Mubarak, or Mohamed Morsy, a U.S.-educated engineer who spent time in Mubarak's jails and offers Egypt a new start as an Islamic democracy.
"We have to vote because these elections are historic," said Amr Omar, voting in Cairo, who said he was a revolutionary youth activist. "I will vote for Morsy... Even if it means electing the hypocritical Islamists, we must break the vicious cycle of Mubarak's police state."
A gunfight killed two in Cairo overnight, according to local media. The reports blamed a dispute between street vendors and there was no apparent connection to the vote, which saw little trouble on Saturday despite mutual accusations of fraud. Observers reported only minor and scattered breaches.
It was impossible to forecast who will emerge the winner by Monday - and whoever it is may face anger and accusations of foul play. Both men have widespread support, but many voters may be staying away, disillusioned by a choice of extremes after centrist candidates were knocked out in the first round last month.
Turnout at polling stations in several areas seemed lower on Saturday than during the first round. Polls re-opened at 8 a.m. on Sunday (0600 GMT).
"I am on my way to vote and I'll spoil my ballot. I'll cross out both Morsy and Shafik because neither deserve to be president," said 40-year-old shop owner Saleh Ashour in Cairo.
The military rulers who pushed out their brother officer Mubarak 16 months ago to appease the street protests of the Arab Spring have already enraged their veteran adversaries in the Brotherhood late last week by dissolving the new parliament, elected only five months ago with a sweeping Islamist majority.
A win for Shafik, 70, who says he has learned the lessons of the revolt and offers security, prosperity and religious tolerance, may prompt Islamist claims of Mubarak-style vote-rigging and street protests by the disillusioned urban youths who made Cairo's Tahrir Square their battleground last year.
"The Egyptian people have chosen freedom and are practising democracy," Morsy said as he cast his vote on Saturday. "The Egyptian people will not back down and I will lead them, God willing, towards stability and retribution."
Shafik, a former fighter pilot and air force chief whose second finish to Morsy in the first round capped a rapid ascent from rank outsider status, made little comment as he voted.
Should Morsy prevail, benefiting from a movement forged by decades of clandestine struggle and from support among those who put aside qualms about Islamic rule to block a return of the old regime, he may be frustrated by an uncooperative military elite, for all the generals' pledges to cede power by July 1.
The Brotherhood on Saturday again denounced the dissolution, based on a ruling by the Mubarak-era constitutional court, as "a coup against the whole democratic process" and insisted only a popular referendum could reverse the parliamentary election.
But though overturning that vote drew comparison with events that triggered the bloody Algerian civil war 20 years ago, the Brotherhood, which hung back in the early days of the 2011 revolution, has shown little appetite for a violent showdown with Egypt's U.S.-equipped army, the biggest in the Arab world.
That stalemate, coupled with a failure this year of legislators to form a consensus body to draft a new constitution and a consequent lack of clarity over the powers the new head of state will have, leaves Egyptians, Western allies and investors perplexed by the prospect of yet more of the uncertainty that has ravaged the economy and seen sporadic flare-ups in violence.
Should Shafik win, his supporters reckon, he and the ruling military council which took sovereign powers when Mubarak quit would work in harmony to restore confidence, notably for the vital and ravaged tourist trade - but questions would remain over how far the Islamists and other opponents would resist.
Casting his vote on Saturday in the New Cairo district of the capital, businessman Ashraf Rashwan, 45, said hostility to the Brotherhood among the generals, who retain power and vast business interests, meant Morsy simply could not govern.
"They'll get no cooperation from the establishment. If Morsy wins, there will be a struggle that Egyptians - me at any rate - aren't ready for," he said. "Shafik will mean smooth transition. He's learned from Mubarak's failure to listen to the people."
One mid-ranking army officer, speaking privately, said he agreed with assessments that the military council would offer far more power to a President Shafik than a President Morsy:
"There will be different treatment depending on who wins. With Shafik, a firm crackdown is sure to happen," he said, noting a decree passed last week which restored powers to the military police to arrest civilians - a measure which replaced a hated emergency law that had lapsed the previous month.
"With Morsy, the establishment itself will not back him and there will be chaos and lax security, all of which will pose challenges to him and could destroy his presidency," he added.
In 60 years since army officers toppled the colonial-era monarchy, Egypt's armed forces have built up massive wealth and commercial interests across industries, helped since the 1970s by a close U.S. alliance which followed the decision of the most populous Arab state to make peace with Israel.
Commonly referred to as the "deep state", it is these shadowy structures, currently overseen in public by the ad hoc Supreme Council of the Armed Forces under Field Marshal Hussein Tantawi, which many Egyptians see maintaining influence long after the promised handover to an elected civilian by July 1.
"There is no doubt that the state in all its institutions - judicial, military, interior, foreign and financial - back Shafik for president and are working to that end," said Hassan Nafaa, a politics professor who campaigned against Mubarak.
"It is very difficult to eradicate this spirit of Mubarak." Only if liberals swallowed their qualms and voted for Morsy to prevent Shafik winning, Nafaa said, "only then may the 'deep state' back down - but I doubt this will happen."
Washington, paymaster of the Egyptian military, and the European Union, a major aid donor, both expressed alarm at the move against parliament and urged the generals to honour their pledge to stand aside. But, like neighbouring Israel, both are also uneasy at the rise of the Brotherhood and have looked on anxiously as Islamists have closed in on power in other new democracies of the Arab Spring, notably in Tunisia and Libya.