President Ilham Aliyev has led the oil-rich Caspian state since 2003, when he succeeded his late father Heydar Aliyev, who had been in power since Soviet times.
Analysts say the referendum to amend the constitution, proposed by the ruling Yeni party, is certain to be passed, allowing Aliyev, 47, to run for re-election when his second five-year term expires in 2013. More than 20 other constitutional amendments are also part of the referendum.
Opposition leaders have urged voters to stay away from the polls, accusing the ruling party of stifling debate in the media and preparing to fix the result.
The opposition says Aliyev wants the constitution changed now despite having more than four years until the next presidential election because the economic crisis, which has caused a dramatic fall in budget revenue amid falling oil prices, threatens his popularity in the longer term.
The president was re-elected last October with 89% of the vote in an election the opposition and international observers said was flawed. The Organization of Security and Cooperation in Europe reported "interference of local authorities, disproportionate use of force to thwart rallies and arbitrary detentions" during the vote.
