Alexey Fedorov, 22, and Alexsey Filatov, 36, admitted breaching the peace on December 5 by fighting in the Gallowgate, Glasgow.
While Filatov pled guilty to resisting arrest, Fedorov, from Moscow, pled not guilty to assaulting a police officer.
The pair will be sentenced in January, at Glasgow Sheriff Court, but Fedorov will be tried on the second charge the following month. They were both remanded in custody until their next court appearance.
Four other Russian fans were also charged with fighting with Celtic fans on the same date. They were bailed pending trial later this month after surrendering their passports.