He was arrested by gardaí on foot of a European arrest warrant and brought before the High Court this afternoon
The 54-year-old is wanted in Northern Ireland to face 18 charges in connection with the alleged abuse of his daughter Aine Tyrell between March 1977 and March 1983.
One of those charges is a charge of rape.
The warrant was issued in January of this year.
The High Court was told that Mr Adams said he would be pleading not guilty.
Liam Adams was escorted by gardaí from the Extradition Section of the Bridewell Garda Station to the High Court this afternoon.
He arrived there by appointment with his solicitor and was arrested at 2.10 this afternoon on foot of a European Arrest Warrant issued on the 26 January this year.
Det Sgt Jim Kirwan told the court that when he told Liam Adams that the warrant related to these alleged offences - he replied 'I just want to say I am not guilty of that. I will be pleading not guilty.'
He said the gardaí were not objecting to bail but had concerns because the allegations were first made in 1987 and the PSNI was contacted again about them in January 2006.
The PSNI was directed to prosecute in January of 2008 but was unable to serve notice on him and he was not there when officers searched his home in December 2009.
But Mr Adams told the court that he did not want to go back to Northern Ireland because he believed he would not get a fair trial there.
He said he had presented himself to the PSNI when he heard they were looking for him and to the gardaí in Sligo in December 2009.
He said he left Northern Ireland in March/April 2009 because his children were in danger and said that the media had treated him disgracefully.
