A running gag in the series featured Gonzo finding something frightening or shocking in unexpected places, such as looking through a door or down a cave to find a big monster roaring or a train coming towards him. Another running gag is his appearances (and misfortunes) in the "Go, Bye Bye!" segments at the end of every episode.
Muppet Babies was also the first time that Gonzo suffered from an identity crisis. Although his species had been indeterminate up to that point (he was sometimes referred to as a Whatever or, more often, a Weirdo), adult Gonzo would not worry about his heritage until Muppets from Space, when it was revealed that he was an alien.