The High Court in Dublin has for the second time began hearing the extradition case of a man wanted by the US on terrorism charges.

Earlier this month Ali Charaf Damache (49), an Algerian-born Irish citizen, won an appeal at the Supreme Court for a judicial review of the DPP’s decision not to prosecute him in Ireland.

The Supreme Court also indicated the case should proceed before a judge other than Mr Justice John Edwards who previously heard the extradition case and had refused leave for judicial review.

Today Mr Damache appeared before the High Court where the recently appointed judge Ms Justice Aileen Donnelly began hearing his case.

Mr Damache, previously with an address in Waterford, is wanted by the US authorities in connection with an alleged conspiracy to provide support to terrorists.

If convicted in the US, he could face up to 45 years in jail, a term his lawyers say would be “a lot more” than could be imposed here.

After the DPP decided in March 2011 not to prosecute him in Ireland, the US sought his extradition in 2012. He has been in custody since, pending the outcome of the extraction matter.

He won the appeal at the Supreme Court against the High Court’s refusal of permission for a judicial review of the decision not to prosecute him here.

The five-judge court unanimously ruled Mr Damache was entitled to judicial review of two issues: whether the DPP’s March 2011 refusal to prosecute him here is reviewable in the circumstances of his case; and was the DPP entitled, in the circumstances of his case, to refuse to give reasons for her refusal.

Chief Justice Ms Justice Susan Denham stressed the court wanted all matters concerning Mr Damache, including the judicial review, extradition and constitutional issues, to proceed to hearing in the High Court as soon as possible.

The court also asked for, and obtained, the consent of the State that issues related to arguments raised by Mr Damache under the Constitution and European Convention on Human Rights should be addressed in tandem with the judicial review.

Mr Damache had twice sought judicial review of the DPP's decision not to prosecute him in Ireland for the offences, but both applications were refused by the High Court.

Last month the Irish Human Rights Commission intervened in the case.

Michael Lynn SC for the IHRC told the court that “the commission is of the view it should intervene.”

He said the Commission wanted to be in a position to make submissions on the human rights issues relating to the case.

Mr Lynn said one potential issue would be his possible detention in a Supermax prison for 40-45 years and the right to practice his Muslim faith.

Mr Damache, who has been living in Ireland for more than 10 years, is wanted on charges alleging conspiracy to provide material support to terrorists and attempted identity theft to facilitate an act of international terrorism.

The US alleges Mr Damache conspired with American woman Colleen LaRose, who used the online name Jihad Jane, and others to create a terror cell in Europe.

LaRose was sentenced last January to 10 years in prison after being convicted of planning to murder Swedish cartoonist Lars Vilks, who had depicted the head of the Muslim prophet Mohammad on a dog.