UEFA last month banned Fenerbahce from next season's Champions League and Besiktas from the Europa League.
The UEFA control and disciplinary body said Fener would be banned from European for three seasons in total, with the third deferred for a probationary period of five years.
CAS confirmed today that Fener had requested they be allowed to compete in the Champions League until their appeal is heard.
A statement from CAS read: "The Court of Arbitration for Sport (CAS) has registered today an appeal filed by Fenerbahce SK and a request for provisional measures filed by Besiktas JK against UEFA in relation to the decisions taken by the UEFA Appeal Body on 10 and 11 July 2013, pursuant to which Fenerbahce SK was excluded from participating in the next two UEFA club competitions it qualifies for, including the 2013/14 UEFA Champions League, and Besiktas JK was declared ineligible to participate in the 2013/14 UEFA Europa League.
"Together with its appeal, Fenerbahce SK filed a request for a stay of the challenged decision."
CAS has not set dates for the hearings.