The Court of Arbitration for Sport heard the case of the 45 Russian athletes - including numerous medal contenders - and two coaches yesterday. It will announce its ruling at 11am, nine hours before the opening ceremony.
Six other Russian athletes' appeals were thrown out. The court said it "lacked jurisdiction" to hear the cases.
The six athletes include two world champion speedskaters, Denis Yuskov and Pavel Kulizhnikov. All of them were originally refused invitations to compete by the International Olympic Committee. Unlike those in the group of 45, all six have previously served bans of various lengths for failed doping tests. The IOC had said it wouldn't invite athletes previously banned for doping.
The first competitions of the games - including a United States versus Russia curling match - had already started when the court heard the cases.
"We are hopeful that the panel will follow our argumentation and respect the rights of the athletes," said Philippe Baertsch, a lawyer for the group of Russians still awaiting their verdict.
In attendance with Baertsch for that hearing were Elena Nikitina, the 2014 bronze medalist in women's skeleton, and Tatiana Ivanova, a luger who won silver in the team event in 2014.
The Russians are seeking to overturn the IOC's decision not to invite them to the games. If they win, it would force the IOC to accept athletes it considers to be linked to doping offenses.
The Russian team is formally banned, so they would have to compete as "Olympic Athletes from Russia" in neutral uniforms under the Olympic flag. With 168 IOC-approved athletes, it's already one of the biggest teams in Pyeongchang.
The IOC won't comment on individual cases, but says its invitation process was based on evidence from a newly obtained Moscow laboratory database detailing doping in previous years.
Other athletes whose cases will be heard include Viktor Ahn, a six-time Olympic gold medalist in short-track speedskating, and Alexander Legkov, a cross-country skiing gold medalist.