The new Nauru Court of Appeal was set to hear their application this week but it has been put off until next year, although a date is yet to be set.
The Nauru 19, which includes a former president of the country, had been charged over an anti-government protest more than three years ago.
In September the group successfully sought a permanent stay on legal proceedings against them, arguing the trial process had dragged on too long and that the government had not met a court order to meet some of the costs.
