McNally, 39, from County Armagh, was serving a life sentence for causing explosions when he escaped with 37 other IRA members in September, 1983.
Most of the Maze escapers were rearrested near the jail, but 19 got away from the area.
McNally appeared before Dublin District Court yesterday afternoon. The father-of-two, wearing a green jacket, cream shirt and jeans, arrived at the court amid high security at 4pm.
Police sergeant Michael Heffernan told the court he arrested McNally at 6.15am. He said he had asked the man who answered the door if he was Dermot McNally and the man replied: "That's me."
Sgt Heffernan said the warrants related to making bombs, possession of bombs and bomb-making equipment, causing explosions, possession of firearms and one count of wounding with intent to commit grievous bodily harm.
In addition, the warrants alleged McNally had been sentenced to 20 years imprisonment for the various offences and that he unlawfully escaped from custody on September 23, 1983.
McNally had been living openly in Sligo after court rulings in the Republic that prevented the extradition of other Maze escapers.
In March, 1990, the Republic's Supreme Court refused to extradite two of the escapers - Dermot Finucane and James Pius Clarke - on the grounds that their offences were political.
McNally, originally from Lurgan, in Co Armagh, was jailed for life in 1977 for causing explosions.
He was given three life sentences for bombing a wine lodge, a post office and a railway station.Reuse content