The High Court in Uganda is hearing an opposition attempt to annul a constitutional amendment which removes presidential age limits.
MPs voted overwhelmingly last year to scrap the age limit of 75.
It meant 73-year-old President Yoweri Museveni, in power for more than 30 years, could seek re-election in 2021.
Opposition lawyers argued that the amendment was "smuggled" into law, and parliament had not followed proper procedures when adopting it.
Security has been increased at the court in the eastern city of Mbale, and some roads have been shut to prevent any unrest.
The opposition has repeatedly accused Mr Museveni of being an authoritarian ruler who wants to cling to power.
His allies say he is a democrat who has guaranteed stability in the East African state.