The Archbishop of Sydney, Anthony Fisher, has told a royal commission the response by Catholic Church leaders to allegations of child sexual abuse amounted to "criminal negligence".

Five of Australia's most senior Catholic figures fronted the Royal Commission into Institutional Responses to Child Sexual Abuse in Sydney on Thursday.

It was the first time Archbishop Fisher had been questioned at the royal commission, which has been running for four years.

"It was a kind of criminal negligence to deal with some of the problems that were staring us in the face," he told a public hearing.

"In other cases, I think there were people that were just like rabbits in the headlights, they just had no idea what to do, and their performance was appalling."

Archbishop Fisher succeeded Cardinal George Pell as the Archbishop of Sydney in 2014.

Catholic Church thought it was 'untouchable'

The Archbishop of Perth, Timothy Costelloe, also gave a damning assessment of the way allegations of sexual abuse had been handled.

He said there had been a "catastrophic failure" in church leadership and that the abuse of children was at odds with what the Catholic Church purported to be.

Catholic Archbishops who gave evidence, clockwise from left: Denis Hart, Philip Wilson, Timothy Costelloe, Anthony Fisher, Mark Coleridge. ( AAP: Catholic Church )

"That leads me to reflect there has also been a catastrophic failure in keeping people faithful [like priests] to the commitments they made. I asked myself what can possibly have gone wrong, or what was missing, that could lead to, not just one, but countless people failing in this way," Archbishop Costelloe said.

The archbishops were grilled about what they had done to deal with those "catastrophic failures" in leadership they had agreed were at the root of the child sexual abuse.

They said they were taking a more collaborative approach to decision-making in their diocese.

"The problem will always be there to potentially rise again unless that issue is dealt with," Archbishop Costelloe said.

He said in the past, the Holy See believed itself to be "so special, so unique and so important" that it was untouchable.

A protest sign outside the Royal Commission into Institutional Responses to Child Sexual Abuse earlier this month. ( ABC News: Billy Cooper )

"That's probably the way many bishops in their own dioceses might also think of themselves — as a law unto themselves, as not having to be answerable to anybody, as not having to consult with anybody as to being able to make decisions just out of their own wisdom," Archbishop Costelloe said.

"That can then trickle down to the priests in the parish. I would see that as one of the major causes of this inability to deal with this terrible crisis."

This is the 50th public hearing of the royal commission.

The Archbishops of Melbourne, Adelaide and Brisbane are also being probed at the hearing.