The court was also holding a separate hearing in a case involving 32 Russian athletes who appealed against their exclusion from the 2018 Winter Olympics in South Korea.
"They request that CAS overturn the IOC decision and allow them to participate in these Games as Olympic Athletes from Russia," CAS said in a statement.
CAS Secretary General Matthieu Reeb told reporters that the hearings would resume at 12:00 (0300 GMT) on Thursday and a final decision could be made by the end of that day.
"The goal is really to finish before the Opening (Ceremony) and well in advance so I would say that for me, the last moment for the announcement should be Friday noon (0300 GMT) but possibly it could already be Thursday evening," Reeb said.
The 15 applicants include cross-country skier Alexander Legkov, who won gold in the 50 km freestyle and silver in the 4x10 km relay at the 2014 Sochi Games, and skeleton athlete Elena Nikitina, who won bronze, among others.
These athletes' lifetime bans from the Olympics for alleged anti-doping rule violations in Sochi were lifted in a CAS ruling last week.
CAS said decisions on the cases will be made in due course, without providing further detail.
Even if the athletes' appeal was successful, it was highly unlikely for any of them to be invited to compete in South Korea.
The IOC last year banned Russia from Pyeongchang for what it called "systematic manipulation" of the anti-doping system at the Sochi Games.
But the Olympic body left the door open to Russian athletes without a history of doping to compete as neutrals at its invitation.
(Reporting by Gabrielle Tétrault-Farber, additional reporting by Tim Hart; Editing by Sudipto Ganguly)
