The controversial constitutional amendment scrapped the 75-year limit imposed on presidential candidates in the East African country, setting up Museveni, in power since 1986, for another bid in 2021.
“We believe the law was passed in error,” Ibrahim Nganda, the opposition chief whip and one of the six MPs challenging the law, told AFP.
The hearing is being held in the city of Mbale, the first time such a constitutional petition has been heard outside of the capital Kampala.
The opposition criticised the change of location, saying it was an attempt to play down the importance of the case.
But the spokesman for Uganda’s judiciary, Solomon Muyita, said the court was sitting in Mbale because it was “deemed convenient”.
Security has been increased around the court in Mbale and several roads have been closed.
“It will take some days to hear the petition, the witnesses and make a ruling,” Muyita said.
The amendment was approved by the parliament, which is dominated by ruling party MPs, on December 20 and Museveni signed it into law on December 27.
It also reimposed a two-term limit on the presidency that was scrapped by ruling party MPs in 2005 allowing Museveni to run for a third, fourth and fifth term in elections widely criticised as being unfair.
But the reimposed term limit would not come into effect until after the next election, allowing Museveni the possibility of running twice more.
Download our app and read this and other great stories on the move. Available for Android and iOS.