Usually on the territory of the country in which you were registered.
For example, in Ukraine, yet during, 5 years old, many were Soviet passports and would not want to change them. But in 1997 then all the forced change on the Ukrainian passport.
In the Baltic countries, Russian speaking population has received the status of non-citizens.
The Pridnestrovian Moldavian Republic, passports of citizens of the USSR acted until 2001.