The university says it will appeal the decision to the Committee on Student-Athlete Reinstatement, an independent panel comprised of representatives from NCAA member colleges, universities and athletic conferences.
The committee can reduce or remove the condition; however, the student-athletes will remain ineligible until the conclusion of the appeals process.
According to TarHeelBlue.com, North Carolina Director of Athletics Dick Baddour said while they respect the decision, the facts of the cases simply did not support permanent ineligibility.
Ramsay, a junior from Red Bank, N.J., played in the first four games of the 2010 season. He was withheld from competition beginning on Oct. 9 and has not returned.
The NCAA enforcement staff will not require UNC to forfeit the two wins in which Ramsay played this year.
Meanwhile, McAdoo --a junior defensive end from Antioch, Tenn.-- has not played this season.