Revd Hassan Abduraheem and Revd Kuwa Shamal (pictured) have been held in custody since May on a number charges including waging war against the state.
The Christian leaders are being investigated for seven crimes in total, including jeopardising national security and espionage.
They face the death penalty if found guilty.
The legal team representing the men have been concerned by what they see as unnecessary delays in the case, with several postponements and adjournments in the trial so far.
Revd Hassan is also being accused of coming to the aid of a man who is thought to be against the government.
Ali Omer was severely burned at a demonstration at Quran Karim University. Some say the incident reflects how government and intelligence forces are increasingly targeting Darfuri students and suppressing peaceful demonstration.
The prosecution says money donated towards Mr Omer's treatment was actually used to support rebel movements in the country.
Sudan:
Leader: President Omar al-Bashir
Population: 41.2 million, 2 million Christians
Main Religion: Islam
Government: Republic
World Watch List Rank: 8
Source of Persecution: Islamic extremism/Dictatorial paranoia
Both the men are orignally from the Nuba Mountains, an area with a significant Christian presence which also wants independence from the Islamist Sudanese government.
Two other men, Petr Jašek and Abdulmonem Abdumawla, are also on trial.
Christian Solidarity Worldwide's Chief Executive Mervyn Thomas said: "We remain concerned by the unjust detention and trial of Reverends Hassan Abduraheem and Kuwa Shamal, Mr Petr Jasek and Mr Abdulmonem Abdumawla.
"The unwarranted delays in the trial, including the three week adjournment, have resulted in the men being held in prison for longer than is necessary.
"We urge the government of Sudan to drop the charges against them without condition or delay.
"We also call for a review of NISS's powers and for the end to the targeting of religious and ethnic minorities in Sudan."
The next hearing is scheduled for 24th October.
