Dame Jenny Shipley and two other directors of collapsed construction firm Mainzeal are appealing a High Court decision that ordered them to pay $6 million each.
Their lawyer Jack Hodder QC at Chapmann Tripp said Dame Jenny, Clive Tilby and Peter Gomm "deeply regretted" the firms' failure, but disagreed with the decision that found they traded the company while it was insolvent for nine years.
"We are appealing on the basis that they were not carrying on the business in the way that was likely to cause serious loss to creditors," Mr Hodder said.
The appeal filed in the Court of Appeal on Tuesday said the High Court breached natural justice and mistakenly applied hindsight to its decision.
Mr Hodder said the court was wrong to conclude that the directors should should have raised concerns over Mainzeal's funding from its parent company Richina and should have resigned before Mainzeal collapsed in 2013 owing $115m to creditors.
"I do not know any case where the law has said that directors need to threaten to resign as part of their obligations."
He wanted to dismiss the directors' liability, and therefore the damages, in full.
"If there is no liability ... then there is no entitlement for anyone to claim money."
Earlier this week, another Mainzeal director Richard Yan also said he was appealing against the High Court decision which ordered him to pay $36 million relating to the company's collapse saying the court made several errors, including its findings relating to liability.
The liquidators from BDO, an accounting and advisory firm, who brought the case were disappointed the defendants filed an appeal but were not surprised.
"It's consistent with the approach that we have had from the defendants to date," co-liquidator Andrew Bethell said.
Mr Bethell said the appeal process would delay payment to creditors and they would consider filing a cross-appeal that increased the damages.
"Our view is that we would prefer a higher number, and I think that is a real risk in the defendants in appealing,"
The liquidators have 10 days to file a cross-appeal.
The defendants appeal is likely to be heard later this year.