Jonathan Idema, Brent Bennett and Edward Caraballo attended a closed-door hearing with four convicted Afghan accomplices.
The three Americans were arrested in July when Afghan security forces raided a house in Kabul being used as a private jail and containing eight Afghan prisoners.
Idema and Bennett were sentenced Sept. 15 to 10 years in jail and Caraballo to eight years.
Idema said his group was tracking down terror suspects with the cooperation of Afghan and U.S. authorities.
The Americans' lawyers were not present at the hearing. Idema complained that U.S. Embassy officials had told them it was "too dangerous to come."
Abdul Latif, one of three judges handling the appeal, said a date for a full court session could not be decided until the defense team was in place.
The trial was often chaotic and translation was poor, according to reporters. On arrival, Idema shouted at the press contingent: "The press lies. None of you tell the truth."
The Americans are serving their sentences in Kabul's Pul-e Charkhi prison, reportedly in a heated and carpeted cell equipped with satellite television.