Azerbaijanis are voting on whether to boost the powers of President Ilham Aliyev, who has ruled since 2003 and cracked down on dissent, the BBC reports.
The plan includes lowering the age limit for presidential candidates, creating a strong vice-presidency and extending the presidential term.
The opposition sees the vote as a move to cement the powers of the first family, with Mr Aliyev’s wife and 19-year-old son seen as potential heirs.
The ruling party dismisses the claims.
The constitutional changes would also create other vice-presidential posts and enable the president to dissolve parliament at any time.
The referendum comes after dozens of opposition activists were arrested in the oil-rich former Soviet state.
One of President Aliyev’s main opponents, Ilgar Mammadov, leader of the pro-Western opposition party ReAL, and other pro-democracy activists are still in jail.