Lawyers in Australia acting for Indian doctor Mohammed Haneef have launched an appeal against the decision to cancel his working visa.
Dr Haneef wants the option to return to work in Australia
Dr Haneef was detained for several weeks in Australia, before a terror charge against him was dropped.
But Australian Immigration Minister Kevin Andrews said he still had suspicions against him.
Dr Haneef is now back in India and did not attend the appeal in Brisbane, which was adjourned until Thursday.
For Dr Haneef, the fight to get back his visa is not only a matter of honour and pride but one of practical necessity, the BBC's Nick Bryant in Sydney says.
He would like to have the option of returning to work in Australia.
Dr Haneef's visa was cancelled after a magistrate in Brisbane granted him bail, a decision which allowed the authorities to keep him in detention.
But even after the charge against him, relating to failed bomb attacks in London and Glasgow at the end of June, was dropped, Australia's immigration minister stuck by his controversial decision.
Kevin Andrews maintained that the Indian doctor had failed what is called the character test, because of his association with alleged criminals.
Mr Andrews continues to say he harbours suspicions about the doctor.
But Dr Haneef's defence team argue that the immigration laws were applied simply to keep him behind bars while the criminal case against him was falling apart, and they insist that this action was improper.
Normally it is hard to win appeals of this kind because the immigration minister has such wide-ranging powers.
But the federal court judge hearing the case has already been critical of Mr Andrews' use of the character test.
By the standard being applied, Justice Jeffrey Spender said that he too would have failed, because he had represented criminals during his career as a barrister.
Details of Dr Haneef's interrogation by Australian police in June have been released on the internet and printed in Australian and Indian newspapers.
Throughout the 142-page transcript, Dr Haneef consistently denies links with the failed car bomb attacks.
"I haven't done any crime... and have not been involved any kind of terrorist activity," he is quoted as saying.
He insists he had no knowledge of the attacks during his time in the UK from March 2004 to July 2006, and never saw any bomb-making equipment.
He also denies receiving training in firearms, explosives or logistics.
But Dr Haneef is said to have told interrogators that during his time in the UK he was in contact with two of the suspects named in the attacks, Kafeel Ahmed and Saleel Ahmed, who are distant cousins on his mother's side.