John Downey, arrested earlier this week in connection with an extradition warrant for offenses involving a 1973 Enniskillen bombing, where two members of the British army were killed, has been granted a guarantee at the Dublin High Court.
Mr. Downey, 66, appeared in court on Tuesday and is detained to date.
Bail was granted today by Ms Justice Aileen Donnelly, subject to the approval of financial guarantees.
Mr. Downey is expected to consolidate later today, once warranty guarantees are obtained.
PSNI is being asked to the north for questioning about two types of murders and a number of help and synergy in an explosion.
The two soldiers of Amsterdam, Alaster, died when an IRA bomb exploded in a car controlled at Enniskillen, Co Fermanagh, on August 25, 1972.
Mr Downey was arrested Monday at his home in Ards, Creeslough, Co Donegal, on the basis of a European arrest warrant.
The full hearing of the extradition request will take place on 23 November.
Mr Downey's trial on charges linked to the 1982 bombing in London's Hyde Park, where four soldiers were killed, collapsed in 2014.
He had wrongly sent a letter from the UK government saying he did not want to question the police when there really was an extraordinary warrant against him.
The trial judge found Mr Downey's arrest at Gatwick airport as he went to the United Kingdom on the way to a vacation, was abusive and left way for any future prosecution in the case of Hyde Park.
The episode triggered a UK government inquiry into the On The Run program.
Mr Downey denied any involvement in the attack on Hyde Park.