The 153 asylum seekers aboard an Australian Customs ship somewhere in the Indian Ocean are being locked up in windowless cabins, their lawyers claim.
Their case, to be processed in Australia, returns to the High Court for a directions hearing in Melbourne on Friday.
They claim because their boat was intercepted 27 kilometres from Christmas Island they were within Australian waters.
The decision not to take them to Australia did not fall within the bounds of "legal reasonableness and it was otherwise disproportionate and therefore invalid", their statement of claims says.
It goes on to say that mothers and children had been separated from their fathers and husbands on the Customs ship, and there was no freedom of movement.
Their phones and belongings have been confiscated apart from the clothes they were wearing.
Almost all the Sri Lankan asylum seekers are unable to communicate in English and none of them have been asked why they left Sri Lanka.
Their lawyers argue their clients should not be returned to Sri Lanka or transferred to offshore immigration detention centres on Nauru or Manus Island in Papua New Guinea.
That's because Nauru and PNG are not signatories to international law principles of non-refoulement, which forbids victims of persecution being returned to their persecutors.
The lawyers are demanding "procedural fairness" and an acknowledgement that border protection authorities acted unlawfully.
Last week the asylum seekers won a temporary reprieve that barred their return to Sri Lanka.
A day later the federal government gave an undertaking to give three days notice before moving the group.
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