The justices declined to review a ruling by a U.S. appeals court in New York which upheld the pair's convictions on 22 of 23 counts of conspiracy and securities and bank fraud.
A jury found the father and son guilty in 2004 of the charges that accused them of concealing loans and stealing millions from the cable operator.
John Rigas, formerly Adelphia's president and chief executive officer, was sentenced in 2005 to 15 years in prison, while Timothy Rigas, the former finance chief, was sentenced to 20 years. They began serving their prison terms last year.
In the appeal, defense attorneys argued that federal prosecutors were required to prove that John and Timothy Rigas had violated Generally Accepted Accounting Principles or call an expert accounting witness in order to convict them of securities fraud.
The attorneys also argued that the reversal by the appeals court of the bank fraud convictions on count 23 for John and Timothy Rigas required the reversal of their bank fraud convictions on count 22.