Allegations of child sex abuse have been made against 26 priests serving in the Derry diocese over the past 50 years, the diocesan bishop has said.
Dr Hegarty expressed his "unreserved apologies"
Dr Seamus Hegarty said there had been only one successful prosecution.
It follows a report which found that 21 priests had abused children in County Wexford over the past 40 years.
Bishop Hegarty investigated past and current child sex abuse allegations with the aid of an independent child welfare expert.
He said they trawled back over 50 years, a period during which 330 priests served or are still serving in the Derry diocese.
Nine of the priests against whom allegations were made are now dead, Dr Hegarty said.
Allegations against 11 of the rest were found to have been withdrawn, not substantiated, mistaken identity, failure to be identified at all, or else determined by the police or social workers not to be a case of child sex abuse, he said.
Of the remainder, one priest was stood down and was professionally assessed to be no risk and another priest paid money to a claimant - though admitted no liability.
In another case, the alleged abuse happened outside Ireland and another case is recent and ongoing, said the bishop.
Two cases resulted in prosecutions and one of these was successful, said Dr Hegarty.
In 1996, Father Gerard McCallion admitted the abuse of two Londonderry sisters years earlier.
Bishop Hegarty said he published the report on Thursday confident that "every allegation made against priests now serving in his diocese had been investigated and the necessary procedures followed".
To the victims, he said he "could not express enough his heartfelt and unreserved apologies".
"I also acknowledge that no system will be perfect," he said.
"However, as Bishop, I will do everything that I can, with the help of national, diocesan and parish structures, to ensure that all reported allegations of abuse are dealt with promptly and effectively.
"Our paramount concern is for the safety and welfare of children," he said.
"An independent child care consultant has recently carried out a review of all cases in this diocese, and the diocese will have ongoing external review."
Meanwhile on Thursday, the Catholic Church authorities in Derry confirmed a parish priest in the diocese had left his post while the police investigated an allegation of child abuse.
A diocesan spokesman said the priest requested a leave of absence during the investigation into the allegation, which the priest denies.
An Irish government inquiry into child abuse in the Ferns diocese in County Wexford uncovered over 100 allegations of sexual abuse by priests.
The 271-page Ferns report published on Tuesday investigated allegations against 21 priests who had been working in the diocese between 1966-2002.
The report said police investigations into claims of abuse were inadequate.
It also criticised bishops in the diocese for failing to take basic precautions to protect children.
Bishop Hegarty said the report had been devastating.
"These innocent people have been wounded so badly by those they should have been able to trust," he said.
"This report is a catalogue of criminal abuse and of sacred trust betrayed."