GARDAÍ, IMMIGRATION officers and the Courts Service are uncertain what to do with two men held in Castlerea Prison who will not reveal their identities.
The pair - one from eastern Europe and the other from Africa - were arrested separately in the west of Ireland, and detained when they could not produce identification papers.
One of the men has told the authorities he would prefer to stay in prison than leave Ireland.
Gardaí have brought in Interpol but even the international police body has been unable to identify the men, who have been behind bars for the past few months.
The African man last appeared at Harristown District Court in Castlerea on Friday morning.
He said that his name was Kebba Nyabally, but he was being detained because gardaí were unable to establish who he was.
The east European, who is believed to be from Latvia, was arrested separately under a public order incident, and was detained when he would not identify himself.
He has told the authorities his name is Alex Smirnous, but he has since refused to co-operate with them.
Supt Sean Ward said that a Garda sergeant had gone to Castlerea Prison to interview Mr Smirnous but he refused to answer any questions.
On Friday, Mr Smirnous told Judge Geoffrey Browne that he did not care how long he was held in the prison after he was remanded in custody for three weeks.
"I don't care; leave me here as long as you want; I don't care if it is 33 weeks," he said through a Russian interpreter.
Det Garda Thomas Breen told Judge Brown that Mr Nyabally had been identified through his fingerprints in England, but under a different name.
He said he had established four different names for the man in custody but could not confirm any of them.
He said he had contacted authorities in Nigeria, Sierra Leone, Gambia and England without success.
Judge Browne noted that neither of the men could be deported because it could not be established where they came from. "But they cannot be left here for the rest of their lives."
Supt Ward said investigations would continue, but that the cases of both men were being hampered because they would not co-operate.
The pair are due to appear before Harristown District Court again on March 28th.