Throughout the two series, Alexei Sayle routinely appeared as many different characters, interjecting his own material into the programme in ways that emulated his stand-up comedy routines.
Alexei Sayle as Jerzei Balowski
His main role was that of the flat's landlord Jerzei (Jeremy) Balowski, which was the only character he reprised, appearing in "Demolition", "Flood" and "Summer Holiday".
Jerzei Balowski in Demolition
Here's a great clip of Alexei as Jerzei from the first episode of the Young Ones.
The Balowski Family
The rest of the time, he was billed as playing various male members of "The Balowski Family", including nephew Alexei Balowski (a protest singer), son Reggie Balowski (an international arms dealer and French Cabaret chanteuse), brother Billy Balowski (a lunatic who believed he was a taxi driver), cousin Tommy Balowski (a drunk), escaped convict Brian Damage Balowski, and a medieval jester "Jester Balowski" (with Helen Lederer as his sidekick).
Alexei Sayle - Dr. Martins Boots
One of the great songs of all time!
Alexei as Billy Balowski
Billy Balowski arrives at the house to deliver an important note, but ends up thirsty. Don't worry though, it's a stunt goldfish!
Alexei as Reggie
Indulges in a bit of cockney patois as they negotiate buying and selling the bomb.
Alexei as a Train Driver
The boys are late for their appearance on University Challenge, because their train driver has been held up by Mexican bandits.
Alexei as Mussolini
He does actually look a little like Mussolini! Here's a look at the funny noises songs.
Alexei as Brian Damage
Possibly the best appearance though, is as Brian Damage. The sarcastic scene is one of those classic British Comedy moments!
Jerzei was apparently Russian, however several times during the series he would break character, or in one case the fourth wall and declare directly to the camera "I'm not really foreign, you know." Also during a discussion between the guys about his nationality Vyvyan comments "He certainly knows a lot about the Mersey sound." - implying he is in fact from Liverpool.
Second Series of The Young Ones
In the second series, Sayle's characters also included a train driver, a Benito Mussolini look-alike (by day the head of the local police force, by night an entrant in the Eurovision Song Contest), and "Harry the Bastard" (manager of the local Rumbelows store, disguised as a South African vampire).