Liberians are voting in a referendum about shortening presidential terms from six to five years and allowing citizens to have dual nationality.
Some of President George Weah’s critics are concerned that he could use the constitutional change to extend the number of terms that he serves.
Liberian presidents are limited to two terms, but constitutional changes in neighbouring Guinea and Ivory Coast meant that the heads of state there could run for third terms despite the term limit still being in place.
Mr Weah’s office has denied that this was his intention, AFP news agency reports.
The repeal of the ban on Liberians holding dual nationality could provide an economic boost, AFP says, as people born in Liberia but now living abroad could then be allowed to own property and provide more investment.