John Downey has been remanded in custody by a judge following his appearance in court in Dublin on Tuesday.
The 66-year-old appeared at the Criminal Courts of Justice in relation to the murder of two Ulster Defence Regiment soldiers in 1972.
Downey was also arrested on suspicion of aiding and abetting an explosion.
He was detained by garda on Monday in Donegal under a European Arrest Warrant as part of a joint operation with the PSNI.
His bail application will take place on Thursday at the Criminal Courts of Justice.
Sinn Fein TDs Martin Ferris, Pearse Doherty, Dessie Ellis and Sean Crowe attended the court hearing.
Speaking after the hearting Donegal TD Doherty said that Mr Downey was a supporter of the peace process and had been told he was not wanted in connection with any offences.
Lance Corporal Alfred Johnston, a father of 4, and Private James Eames, a father of 3, died when a device exploded in a car they were checking on the Irvinestown Road, Cherrymount, Enniskillen on August 25, 1972.
In 2014 Downey stood trial for the 1982 Hyde Park bombings in which four soldiers were killed and a number of people were injured.
The trial collapsed because Downey had been mistakenly awarded an "on-the-run" letter by the UK Government which said he was not wanted by police.
He has always denied being involved in the Hyde Park attack.