Voters face a stark choice between a conservative Islamist and a former military officer who served ousted autocrat Hosni Mubarak.
Reeling from a court order two days ago to dissolve a new parliament dominated by the Muslim Brotherhood, many question whether the wealthy generals who pushed aside Mr Mubarak last year to appease the pro-democracy protests of the Arab Spring will honour a pledge to let civilians rule.
With neither a parliament nor a new constitution in place to define the president's powers, voting this weekend will not settle the matter, leaving 82 million Egyptians, foreign investors and allies in the United States and Europe unsure what kind of state the most populous Arab nation will be.
For those who preferred the secular centrists, leftists and moderate Islamists who lost in the first round, the two-man run-off leaves an unpalatable choice from the extremes.
Some of Egypt's 50 million eligible voters say they will despoil their ballots rather than back Ahmed Shafik (70), a former air force commander who was Mr Mubarak's last prime minister, or Mohammed Morsy (60) of the Brotherhood, the clandestine enemy of army rule for six decades.
But many were determined to make their voice heard. Queues formed early at some polling stations as they opened at 8am (0600 GMT) for the first of two days of voting. A result could be known as early as tomorrow night, after the second day's vote.