EU nationals are among those liable for deportation under new legislation introduced by the Minister for Justice.
The Immigration Bill includes a provision for the deportation of EU nationals "whose conduct is such that it would be contrary to public policy or endanger national security to permit them to remain in the State".
Mr O'Donoghue said the Bill deals with the "principles governing the power to deport and the procedures to ensure that the rights of individuals are respected when deportation is being contemplated in any case".
Those who can be deported will include "those whose deportation would be conducive to the common good".
Non-nationals whose asylum applications have been transferred to another "Convention" country - the first EU country they arrived in - are included.
Asylum-seekers whose applications are refused are also on the list, as are those "in contravention of the requirements of immigration law" and people who have served or are serving prison sentences. Those whose deportation has been recommended by a court in criminal proceedings are also liable for deportation.
Fine Gael's justice spokesman, Mr Jim Higgins, criticised the Bill's title as totally misleading and said it had nothing to do with immigration.
"It has to do with deportations of aliens from this country," he said. "The Bill should be called the Deportation Bill."
It was another "stop gap effort" when what was needed "is a coherent refugee /asylum policy".