The names of many priests found guilty of child sex abuse are not on the Republic's sex offenders' register because it was established after they were convicted.
As a result, the whereabouts of many of the priests named in the report -- both those who were convicted and those who were suspected of carrying out abuse -- is unknown.
Among them is Fr William Carney, a serial abuser. He was the subject of 32 complaints of abuse to the Dublin Archdiocese. He is believed to have moved to Scotland and to have married. However, other reports have indicated that he has since moved to Birmingham.
Another child abuser, Ivan Payne, vanished after being released from prison in 2002.
Payne had pleaded guilty in 1998 to charges of indecent assault on 10 young victims and was sentenced to serve six years' imprisonment.
After his release he moved to Britain and earlier this year, it emerged that the 65-year-old laicised priest was living in the Welsh town of Aberdare. However, when locals learned about his past Payne went into hiding.
A handful of priests named in the damning Murphy report are on the sex offenders' register and are obliged to tell gardai of their movements. If they fail to fulfil that condition, they face a jail sentence or a fine.
However, Carney and Payne are not on the register because their convictions were prior to 2002.
Abuse victims have called for a list of known abusers to be drawn up by the Catholic hierarchy and handed over to gardai.
"There's no doubt that the abuses could continue if these men aren't watched," said Michael O'Brien of Right to Peace last night.
"A paedophile is a paedophile and they don't change.
"The Church must wake up and give the gardai a list of these people. . . so that they don't abuse again," he said.
John Kelly, of Survivors of Child Abuse, said the Irish government needed to introduce new legislation.
He said he recently saw a former priest, who he knows abused a number of young boys, walking down the street.
"This man is not being monitored or supervised, he is just one of many," he added.
The Dublin Diocesan office did not return calls for comment last night.