After Soviet union has split to many independent countires, the main role and the legacy of the Soviet space program was taken by Russia. Russia had to made an agreement with Kazakhstan since the Baikanur, main soviet launch place and soviet space center became part of the new country Kazakhstan. Besides Russia Ukraina and Kazakhstan also established their space agencies. Kazakhstan even became an owner of the Buran space shuttle. But only russian space program was and still is contionuosly in the run. Russian space agency is called Roscosmos.
In first few years after 1992 kosmonauts were using the same model of Poljot 3133 chronograps as in Soviet Union. But since Russia became more open to the western world and Poljot hasn't done any new development, in 1995 Fortis entered into the russian space program. But from the pictures of the kosmonauts it is obvious, that also other watches were used (for example Omega X33).