Advocates argue that Australian law does not give the Federal Government the power to imprison people in other countries.
Refugee advocates are taking their fight to the highest court in the land, focusing on Australia's asylum-seeker policies.
The case is on behalf of a woman from Bangladesh who was brought to Australia from Nauru during her late stages of pregnancy 10 months ago.
Daniel Webb is the director of legal advocacy at the Human Rights Law Centre.
"An incredibly vulnerable woman. She's been detained on Nauru previously and she's been brought back to Australia for some urgent medical treatment. This woman has a ten month old baby daughter and she is terrified that she and her baby daughter are going to be sent back to an offshore environment. That's already caused her a great deal of harm."
It seems to have proven an effective deterrent to people-smuggling but the legality of offshore processing is part of the challenge.
Lawyers are arguing that Australian law doesn't give the Commonwealth power to imprison people in other countries.
"There remain important and untested constitutional questions about the power of the Australian Government to pay and to control the detention of innocent people in other countries," says Daniel Webb.
Former Immigration Minister Scott Morrison says the present policy is vital.
"Our border protection regime has been incredibly successful, it has saved lives. It has ended the terrible cost that was being incurred and has ensured integrity of our refugee and humanitarian program which enabled us recently to commit to 12,000 additional refugees and humanitarian entrants coming in response to the Syria crisis."
The loopholes in the Commonwealth's funding of offshore processing centres were closed recently with the passage of emergency legislation supported by federal Labor.
And this week the doors of Nauru's processing centre were flung open, allowing those within to move freely with the added promise to process all 600 outstanding asylum-seeker claims within a week.
Months of deliberation is expected to follow the hearing's second day on Thursday.
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