The athletes were among 43 disqualified from events, banned from participating in future Olympics and in some cases stripped of their medals following the IOC's investigation of widespread doping in Sochi exposed by an independent report for the World Anti-Doping Agency.
Maxim Belugin, part of the two and four-man bobsleigh teams which finished fourth at Sochi 2014, looks to be the only athlete not to have filed an appeal.
CAS said the cases will all be heard together in the week beginning Jan. 22 and expects verdicts to be issued by Jan. 31.
That is nine days before the start of this year's Games in Pyeongchang, South Korea and three days after the International Olympic Committee's deadline for entries, other than those in exceptional circumstances.
The IOC last month banned Russia from the Pyeongchang Games as a result of its "unprecedented systematic manipulation" of the anti-doping system, though individual athletes will be able to compete effectively as neutrals if they can prove their anti-doping credentials.
(Reporting by Mitch Phillips, editing by Ed Osmond)
