Congo-Brazzaville is holding a referendum on constitutional changes that would allow President Denis Sassou Nguesso to stand for a third term.
Opposition leaders have called for a boycott after a number of protesters died in clashes with security forces.
Under the current constitution, the president cannot seek re-election because he is over the age of 70 and has already served two terms.
President Sassou Nguesso first came to power in 1979.
He is now coming to the end of his second seven-year term. He won the last election 2009 with nearly 79% of the vote in a poll boycotted by half the opposition candidates.
Turnout is said to have been low in the capital Brazzaville.
One opposition leader, Rene Serge Blanchard Oba, said he had not voted "because to do so is to encourage the power of this foolishness", the Associated Press news agency reports.
But after casting his ballot, President Sassou Nguesso denied that the proposed changes were about him personally.
"We want change in order to have a constitution of the future, and not as others claim for superficial reasons because the president craves a new mandate," the AFP news quotes him as saying.
The result is not expected for several days.
Tens of thousands of people took part in a peaceful demonstration against the referendum in September.
Four people died on Tuesday, when security forces dispersed further protests in Brazzaville and the economic capital Pointe-Noire.
Protesters told the BBC the security forces had used live ammunition and that army helicopters had been deployed. Several activists and opposition leaders reported arrests and intimidation.
The outcome of Sunday's vote and the Congolese people's response to it will be watched closely in the region, as presidents in the neighbouring Democratic Republic of Congo and Rwanda are also expected to try to run for third terms in forthcoming elections, the BBC's Maud Jullien reports.
There have been months of unrest in Burundi, where President Pierre Nkurunziza was re-elected for a controversial third term in July.
Africa's longest-serving leaders:
- 36 years: Teodoro Obiang Nguema Mbasogo - Equatorial Guinea, took power in a coup in August 1979
- 36 years: Jose Eduardo dos Santos - Angola, took over after death of the country's first president in September 1979
- 35 years: Robert Mugabe - Zimbabwe, won the country's independence elections in April 1980
- 32 years: Paul Biya - Cameroon, took over after resignation of the country's first president in November 1982
- 31 years: Denis Sassou Nguesso - Congo, installed by the military in October 1979, out of power from August 1992-October 1997
- 29 years: Yoweri Museveni - Uganda, became president after his rebel group took power in January 1986
Among the changes being voted on are scrapping the presidential age and two-term limits.
Texting and internet services were cut and public meetings banned ahead of the referendum, residents said.
The opposition have been campaigning under the slogan "Sassoufit", a pun on the French expression for "that's enough" (ca suffit).