The Transport Workers Union (TWU) is challenging a court order to pay Qantas more than $750,000 in compensation over strikes at four Australian airports.
Qantas ground staff belonging to the TWU held four-hour work stoppages at Sydney, Brisbane, Adelaide and Perth airports on the morning of March 30, 2009.
The industrial action, which caused widespread delays, was in protest at Qantas hiring casual staff.
But the Federal Court ruled in May 2011 that the stoppages contravened the Workplace Relations Act 1996.
Two months later, Justice Michael Moore ordered the TWU to pay Qantas $707,345 plus interest in compensation, and $20,000 in penalties.
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Six TWU officials, including national secretary Tony Sheldon, were personally ordered to pay Qantas an additional $18,000 in penalties.
The TWU appeared in the Federal Court in Sydney on Monday to launch an appeal against the payment of the compensation component.
The union's lawyer, Adam Hatcher, argued the court did not have the power to order payment of the compensation.
"Our submission, on the appeal, is that the provision is not authorised," Mr Hatcher told the court.
"We are not concerned with the quantification of the amount, merely the order."
The TWU is not appealing the penalties component nor the Federal Court's ruling that the work stoppages were illegal.
The case, before Federal Court justices Peter Gray, Robert Buchanan and Neil McKerracher, is continuing.
