A CAS source told the news agency TASS that a hearing into cases of all 32 applicants will be held on Wednesday. The date when the decision will be announced is not yet known, it reported.
A total of 168 Russian athletes were invited to take part in the Olympics, although the Russian Olympic Committee initially applied for 500.
On Tuesday, 32 Russian athletes, including biathlete Anton Shipulin, cross-country skier Sergei Ustyugov and short-track speed-skater Viktor Ahn appealed their non-invitation at CAS.
As the IOC has suspended the membership of the Russian Olympic Committee, Russians will take part in the 2018 Winter Olympic Games under the status of neutral athletes (OAR, which stands for "Olympic Athlete from Russia").
The 2018 Winter Games will be held in PyeongChang, South Korea, from February 9 to 25.
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