The athletes were among 43 disqualified from their events, banned from participating in future Olympics and in some cases stripped of their medals following the International Olympic Committee’s investigation of widespread doping in Sochi.
The IOC has banned Russia from the Pyeongchang Winter Games next month as a result of its "unprecedented systematic manipulation" of the anti-doping system. However, individual Russian athletes will be able to compete as neutrals if they can prove their anti-doping credentials.
Russia has repeatedly denied any state involvement in the doping which was exposed by an independent report commissioned by the World Anti-Doping Agency (WADA).
Lawyers representing the athletes said in a statement that they had been banned "despite a lack of specific evidence against any of them and in breach of their fundamental due process rights."
"The athletes are hopeful that the CAS Panels will grant them a fair hearing."
The banned athletes compete in speed skating, bobsleigh, skeleton, cross-country skiing, ice hockey, luge and biathlon.
CAS said that Grigory Rodchenkov, Russia's former anti-doping chief who turned whistleblower, and Richard McLaren, the Canadian sports lawyer who wrote the WADA report, were expected to testify by video or telephone.
CAS secretary general Matthieu Reeb said that three speed skaters would be the first of the 39 athletes to address the hearing on Monday.
"(The 39 athletes) will be heard one by one during the week. I can confirm that the hearing will last at least until next Saturday," he told reporters. A decision is due by Jan. 31 - nine days before the start of this year's games in Pyeongchang.
CAS has said it received applications from 42 of the 43 banned athletes and that the cases involving three biathletes had been suspended and would not be heard this week.
Maxim Belugin, part of the two and four-man bobsleigh teams which finished fourth at Sochi 2014, is the only banned athlete not to have lodged an appeal.
(Writing by Brian Homewood; Editing by Richard Balmforth)
