The High Court has ordered the committal to prison of Peter Darragh Quinn and Seán Quinn Jnr for three months for contempt.
Any punitive orders against bankrupt businessman Seán Quinn Snr have been held over to allow him time to comply with court orders.
The three men had until midnight last night to reverse steps they had taken to put international assets out of the reach of the former Anglo Irish Bank.
They were found guilty of contempt of court at the end of last month.
Seán Quinn Jnr and his cousin have been told they can purge the contempt at any time.
Seán Quinn Jnr has begun his sentence this evening.
In her ruling, Miss Justice Elizabeth Dunne said she was not happy with the level of cooperation by the Quinns with court orders.
She said evidence presented to the court today reinforced her feeling there was a lack of openness by them.
She said video footage showing Mr Quinn's son and nephew at a meeting in Ukraine in January, discussing how a significant payment could be made to them, did not assist the case.
She rejected suggestions by the Quinns' lawyers that they were being intimidated at the meeting in Kiev.
The High Court earlier issued a warrant for the arrest of Peter Daragh Quinn, the nephew of Séan Quinn, after he failed to appear for the hearing.
The court made the order after hearing that all efforts to contact him this morning had failed.
One message had been received that he was sick, but the judge said no evidence of illness had been brought to court.
Lawyers for the Quinns said Peter Darragh Quinn had sworn affidavits between 2am and 3am today and he appeared to be ok.
Earlier, lawyers for IBRC told the High Court that the three seemed to have adopted the position they could go to jail for a short time and keep €500m of assets.
IBRC had asked the court to consider sending Seán Quinn Jnr and Peter Darragh Quinn to jail for contempt while leaving Seán Quinn free to comply with court orders.
However, Senior Counsel Bill Shipsey for the Quinns said the two younger men would be best placed to assist the bank in a meaningful way to comply with court orders.
Senior Counsel Paul Gallagher said nothing material had been done to return assets.
The Quinns admit the bank is owed €455m, but are disputing a claim by IBRC for a further €2.5bn.