The group's ringleader Jonathan 'Jack' Idema, described by US media as a bounty hunter, cursed reporters as he arrived at a court in the Afghan capital, dressed in military-style khaki trousers and shirt and dark sunglasses.
"The press lies. None of you tell the truth," Idema, 48, said as he entered the closed-door hearing.
Fellow appellant Brent Bennett, 28, was with him. Edward Caraballo, 42, who said he was a freelance journalist making a documentary on their activities, arrived later.
Monday's session was a preliminary hearing only, a court official said.
"They didn't bring their lawyers to this session. That's why we delayed our session. We cannot take a decision in this meeting," Abdel Latif, a judge at the Domestic and Foreign Crime Intelligence Appeals Court, told reporters outside.
Idema's lawyer John Tiffany earlier said he would appeal the case on the basis that the appellants had not been given a fair hearing. But he was not with them for the first day of the hearing.
On leaving the court Idema praised the justice ministry.
"The ministry of justice and this court has been very kind to us. I must say much kinder than our previous [appearance]," he said.
The trio, arrested in July, were convicted on September 15 after being found guilty of running a private prison in Kabul and torturing at least eight Afghan suspects as part of a vigilante counter-terror operation.
Idema and Bennett were sentenced to 10 years jail in Kabul, and Caraballo was given eight years.
They have served the first part of their sentences in Kabul's Pul-e-Charkhi jail - a prison which houses many of the Taliban prisoners that Idema and his group claimed to be hunting.
Their four Afghan accomplices, who were sentenced to between one and five years in prison, also appeared in court for the appeal.
There was speculation that the trio might be transferred to the United States or win release on appeal after Afghanistan's October election which was won by President Hamid Karzai.
Idema has claimed that he was carrying out anti-terrorism operations in coordination with the US Defense Department and Afghan authorities, a claim denied by both governments.
International peacekeeping troops deployed in Afghanistan have confirmed that they assisted Idema on three separate raids, on the presumption that he was a member of the US special forces.
The group had also handed over a suspected terrorist to the US-led coalition in Afghanistan. The man was later released.
The case illuminated the shadowy world of private security contractors in Afghanistan and strengthened calls by rights groups for the US-led military to open its detention centers to independent inspection.
Idema's trial was marked by chaotic scenes and was adjourned several times.
© 2004 Agence France-Presse
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