If he wins President Al Sisi could stay in power until 2030 and the role of the already powerful military would be boosted too.
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Egyptians voted in a referendum on Saturday which decides whether President Abdel El Fatta Al Sisi's term in office should be extended from four to six years - and whether he should be legally allowed to run for a third time.
Parliament has already approved the constitutional amendments and pollsters predict the three-day referendum will too.
If it happens Al Sisi could stay in power until 2030 and the role of the already powerful military would be boosted too.
Observers say the size of the turnout will be watched as a test of Sisi's popularity, which has been dented by economic austerity measures since 2016.
Sisi's supporters say the changes are needed to give him more time to complete major development projects and economic reforms.
But his critics say they'll concentrate more powers in Sisi's hands and return Egypt to an authoritarian state and human rights groups agree.
When he was still a general in 2013 Al Sisi overthrew Egypt's first democratically elected president, Mohamed Mursi, a Muslim Brotherhood leader.
Mursi was elected after Egypt's long-time autocratic leader Hosni Mubarak was overthrown in 2011 after nationwide protests. He'd been in power for nearly thirty years and, like Al Sisi, was a member of the military.