The Costina family, from Bistrita in northern Romania, applied for political asylum when they arrived at Shannon Airport on a flight from Moscow in January 1994.
Mr Costina, now 40, is an architect who had been working as a rocket engineer in the Romanian army. He was accompanied by his wife, Sylvia, and their sons, Ionus and Marius, then aged seven and 12.
Both his brother's family and her brother's family arrived on the same plane and applied for asylum at the same time. The other two families have been allowed to stay and have been given work permits.
After six months in Ennis, the Costinas moved to west Dublin, where the two boys went to St Francis Xavier's National School in Clonsilla.
Ms Irene Corrigan, who taught Ionus there, calls them "a very good and conscientious family, very concerned with their children's education and well-being".
Their first application for asylum was refused in late 1994. Their appeal against this decision was turned down last year. Last January they applied to the Minister for Justice, Mr O'Donoghue, for leave to stay on humanitarian grounds, an executive decision he has the power to make.
However, they had received no response before their arrests last Thursday. A deportation order dated October 20th was sent to their solicitor, but the first Mr Costina knew about it was when he was handed faxed copies of the orders as he left Store Street Garda station on Thursday.
Since then friends, neighbours and clergy in west Dublin have mounted a campaign to prevent their deportation. Local politicians such as the Independent Socialist, Mr Joe Higgins TD, and the former Labour TD, Ms Joan Burton, also became involved. A petition containing 600 local signatures was handed to the Taoiseach, Mr Ahern, at Parnell Park yesterday by the Dublin football team's physiotherapist, Ms Judy Murphy, a friend of the family.
The parish priest at Laurel Lodge in Castleknock, Father Eugene Kennedy, was applauded when he spoke in their favour at Mass yesterday.
Father Kennedy was one of six local clergymen who wrote an open letter to the Taoiseach at the weekend appealing to him to allow the family to stay in Ireland.
They wrote that the two boys "have become `Irish'. All of their formative years have been spent here. Their only friends are here. Marius is due to sit his Leaving Certificate examination next year. Their only future is here. They attend the local school, play Gaelic football and speak with Dublin accents."
The clergy called the Department of Justice decision to deport the family "totally against natural justice and common decency", in particular as it was the Department which "in the first place allowed the children to grow up here for the past five years."