Mark Kerr, 24, and Tony Taylor, 44, deny the charges of possessing a firearm with intent to endanger life.
They were detained on Wednesday evening after police officers forced a red Peugoet off the road.
The car was driven by Kerr, of Carranbane Walk in the Shantallow area of the city. Officers found a rifle inside a red sports bag in the boot of Kerr's car.
A subsequent search of the vehicle uncovered four feet of detonating cord under the back seat.
Taylor, of Bishop Street, was arrested in a nearby alleyway in a follow-up operation. Police believe wrapping found in the 44-year-old's pocket was linked to the red sports bag.
A detective told the court that during police interviews Taylor said he had been involved in a row with a motorist who'd thrown the plastic wrapping at him and he'd picked it up and put it in his pocket.
Kerr told police he had been acting under duress when he drove his car, and denied being a member of any illegal organisation.
The court heard a security operation was launched in Derry on Wednesday after police received a tip-off about IRA activity in the area.
The army bomb squad was called to the Foyle Road area and three coffee-jar type devices were found in the area.
A lawyer for Mark Kerr claimed his client had no relevant criminal record and it would be unusual for paramilitaries to use their own car to transport weapons.
Both men have been remanded in custody.
Supporters applauded and called out as the pair were led away.