A series of four films was directed by Mikhail Zaytsev. It was his first time as director (apart from a 37-second anti-AIDS PSA made two years earlier). I have here added English subtitles to the first two films (#1 also has Russian subtitles, if you select them). They're not masterpieces, but representative of the era and pretty funny.
"Captain Pronin - Major Pronin's Grandson" (1992)
(if you're wondering who Major Pronin is, he starred in several James Bond-like books written from 1939-1962 by Soviet writer Lev Ovalov. There's a Russian-language Wikipedia article about him over here)
"Captain Pronin in America" (1993)
My favourite part of the second film might be its poke at Western gender equality (the wrestlers).
The last two films in the series were weirder and not as funny, in my opinion.
Here are the translated lyrics of the rather catchy song...
Captain Pronin: foe of lawless clans
Everyone knows him in foreign lands.
Russian Super! Captain Pronin
cracks the case, loves the chase. He's owning!
Captain Pronin - sleuthing ace. Even kids will tell you
He provides the highest class, super-detective.
Captain Pronin — superstar, no one doubts his value.
Day and night, for you and me, his unseen fight keeps us free!