Eamonn Walsh and Raymond Field, both auxiliary bishops in Dublin, released a joint statement that was read during midnight mass, the BBC reported Friday.
The Murphy Report named five bishops who allegedly failed to deal with priests associated with sexual misconduct charges. Four of the five have now said they will step down, with Martin Drennan, the bishop of Galway the only exception.
James Moriarty announced Wednesday he had sent his resignation as bishop of Kildare to the Vatican. Pope Benedict XVI is expected to accept it.
Donal Murray resigned last month as bishop of Limerick.
In their statement, Field and Walsh said they hoped their decision would help those who had been molested by priests.
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