Last month all of Chile's active bishops offered to quit for collectively failing to protect children from paedophile priests.
The Vatican announced that Francis was allowing Rancagua Bishop Alejandro Goic Karmelic and Talca Bishop Horacio del Carmen Valenzuela Abarca to resign.
That brings to five the total of resignations accepted so far out of the 31 offered.
In the region of the Rancagua diocese, 14 priests have been accused of having had sex with minors. Bishop Goic had served as head of the Chilean church's child protection commission.
Francis had already accepted the resignation of Osorno Bishop Juan Barros, once a top aide to Chile's most notorious priest.
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