Rev Hassan Abduraheem and Rev Kuwa Shamal are accused of seven different charges which range from spying to lying about persecution.
Some of the charges against carry the death penalty as the maximum sentence.
It's reported the prosecution is calling for the "harshest punishment" available.
Sudan is predominantly Islamic, with the mainly Christian part breaking away to become South Sudan in 2011.
The President of Sudan, Omar al-Bashir has said the country is an Islamic state governed by sharia law. He is wanted by the International Criminal Court over genocide claims.
The trial of the pastors continues.
