On Tuesday, 426 independents will be competing for 213 seats in 99 constituencies in the run-offs in Cairo and 12 other governorates.
Egyptian expatriate voters are casting their ballots on Monday and Tuesday while voters at home head to the polling stations on Tuesday and Wednesday.
Polls at home opened at 9am local time and are scheduled to close at 9pm.
Former interim president Adly Mansour cast his vote in a school in Cairo's Heliopolis district.
There have been reports that there is a delay in opening 107 primary polling stations in the Delta's Menoufiya governorate, according to Al-Ahram website.
In the first round of the second stage of the election, as many as 2,893 candidates competed to fill 222 seats reserved for independents, and 195 vied for 60 seats reserved for party-based candidates.
The electoral coalition entitled For the Love of Egypt won the 60 seats reserved for party lists, and only nine of the 222 seats reserved for independent candidates were won outright.
The polls are taking place under tight security by police and armed forces.
In North Sinai, special security units transported judges to their polling stations in the restive Al-Arish city. Seven people, including a judge supervising the second stage of the elections, were killed on 24 Novemeber in an attack at an Al-Arish hotel claimed by Daesh-affiliated Sinai Province, formerly Ansar Beit Al-Maqdis.
The Free Egyptians Party, founded by business tycoon Naguib Sawiris, will have the highest number of candidates in the run-offs, with 52 out of 110 making it to the second round.
The Future of Homeland Party is second in line with 50 out of 89 candidates.
Forty-three candidates out of 135 affiliated with the Wafd Party, Egypt's oldest liberal party, qualified for the run-off round.
The National Centre for Research and Consultants noted that 19 out of a total 168 female candidates qualified for the run-off round, and a record 61 women have so far gained seats in parliament, with 33 in the first stage and 28 in the first round of the second stage.
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