Detective Garda Brian Power told the court that he had arrested Mulcahy outside Mountjoy Garda Station on the North Circular Road yesterday morning.
He said he arrested him for possession of a firearm in suspicious circumstances the day before on Temple Street in Dublin and for membership of the IRA on the same occasion.
Mulcahy wore a blue jacket and jeans as the charges were put to him again in court.
He was charged with the unlawful possession of one 9mm Parabellum calibre Beretta Model 9000S semi-automatic pistol. He was also charged with membership of an unlawful organisation, styling itself the IRA.
Mr Justice Paul Butler remanded him in custody to come before the court again on Tuesday, when it's expected a bail application will be made.