John Rigas, 82, was sentenced in June 2005 to 15 years in prison, and Timothy Rigas, 51, the company's former finance chief, was sentenced to 20 years. Both men have remained free on bail while they pursued their appeals.
At the time, U.S. District Judge Leonard Sand in Manhattan admonished the elder Rigas for his lack of remorse and said he would have imposed a lengthier prison term if not for Rigas' age and ill health.
The Adelphia case was one of the biggest corporate fraud prosecutions in recent years. The father and son were accused of looting the company to pay for personal land deals and vacation homes.
In its decision Thursday, a three-judge panel of the U.S. Court of Appeals for the 2nd Circuit said the defendants needed to show substantial errors by the district court for a reversal of the jury verdict.
"Given the weight of evidence supporting the jury's verdict on each charge, we conclude that they have not done so," the judges said.
Attorneys for the Rigases had no immediate comment on the ruling, nor did the U.S. attorney's office in New York, which prosecuted the case.
Adelphia filed for bankruptcy protection in June 2002. Its cable assets have been sold to Comcast Corp. and Time Warner Inc.