The Northern Ireland peace process is based upon membership of the European Union, the High Court has heard.
Lawyers mounting legal challenges to Brexit insisted the case was one of significant constitutional importance.
Separate proceedings have been issued by the father of a loyalist paramilitary murder victim and a cross-party group of MLAs.
Raymond McCord and politicians including David Ford, Colum Eastwood, John O'Dowd and Steven Agnew are seeking to judicially review the British Government's move towards leaving the EU.
They claim it would be unlawful to trigger Article 50 of the Lisbon Treaty - the formal process for confirming the UK's exit - without first securing Parliamentary authorisation.
Similar legal challenges are already underway in London. But a judge in Belfast was told on Monday there are issues and implications specific to Northern Ireland.
It's clearly a matter of some gravity and constitutional importance, not just for England and Wales, but particularly for Northern Ireland. The very basis of the peace process and the Good Friday Agreement, we say, is based upon the membership of both states (UK and Ireland) to the European Union.
Both cases centre on the Government's response to the 23 June referendum result.
Even though the UK overall voted narrowly to leave, a 56% majority in Northern Ireland wanted to remain.
Mr McCord's legal team contend Brexit will undermine the UK's domestic and international treaty obligations under the Good Friday peace accord.
The campaigner, whose son Raymond McCord Jr was murdered by the UVF in north Belfast in 1997, is taking the case amid concerns that European peace money which goes towards victims of the Troubles may be discontinued.
The MLAs, backed by representatives of the voluntary and community sector in Northern Ireland, are also contesting the legality of the process.
They have identified a series of obligations that must be satisfied before Article 50 can be triggered, including requirements for Parliamentary legislation and the consent of the Northern Ireland Assembly.
Mr Eastwood, the SDLP leader, Alliance MLA Mr Ford, and Sinn Féin representative John O'Dowd all joined Mr McCord in court for the brief hearing.
Discussions centred on whether their challenges should focus on issues specific to Northern Ireland, while other proceedings continue in England.
Although Prime Minister Theresa May has indicated Article 50 will not be triggered before the end of this year, Mr Justice Maguire was told proceedings should be "expedited".
Tony McGleenan QC, for the Government, said: "There's a desire to conclude any litigation by the end of 2016."
Following submissions the judge decided to list the cases for mention again on Thursday.Outside court, Mr O'Dowd claimed the legal challenge was being taken to protect the rights of the 56% in Northern Ireland who voted to remain.
He said: "This is probably one of the most important constitutional cases that has been heard here for decades."
Mr McCord expressed fears for the potential impact on the Good Friday Agreement.
He added: "There's no way that victims are going to trust the British Government that funding will remain in place."