The exact name of Gonzo's species has never been revealed. The character originally evolved from Snarl, a frackle from The Great Santa Claus Switch. However when "The Great Gonzo" appeared on the The Muppet Show the frackle species trait did not carry over. In episode 223, John Cleese referred to Gonzo as "the ugly, disgusting little blue creature who catches cannonballs." And in The Muppet Movie, Kermit said that Gonzo looked "a little like a turkey," to which his conscience replied, "Yeah, a little like a turkey, but not much." In 1985 a collection of Muppet comic strips were released in a book titled "Chickens are People, Too!...But what are Gonzos?". The Muppet Babies also tackled the subject with the book What's a Gonzo?. In the late 90s, the question was posed in the Ask Henson.com web column, "What exactly is Gonzo?" Dave Goelz responded: "Nobody knows except his parents, and they're not talking. It was always one of those taboo subjects around the dinner table." Gonzo the "Whatever" It was in 1981 during The Great Muppet Caper that Gonzo solidified himself as a formal "Whatever." When Kermit, Fozzie and Gonzo were shipped to England in crates. Kermit's crate was labeled "Frog", Fozzie's was "Bear", and Gonzo's crate read "Whatever." "Whatever" was used thereafter whenever Gonzo's species came into question. In one of the later Muppet comic strips, Gonzo is seen walking past a "Men" and "Women" bathroom to enter a third door labeled "Whatevers". He was called a "Whatever" in The Muppets Take Manhattan and Muppet Treasure Island. In Muppets From Space, Gonzo told Noah to put him down as a "Whatever" in his dream. Gonzo the "Weirdo" On Muppet Babies, Gonzo's species was often cited as "Weirdo." However, in the episode "What's New at the Zoo?," Gonzo eventually became worried that he was an endangered species, and briefly imagined himself as an anteater. In "Fozzie's Family Tree," Gonzo imagined that he came from another planet and his family sent him to Earth because everything on his home planet was turning normal, and his parents didn't want him to become normal. Gonzo the Alien In Muppets from Space, Gonzo began to have disturbing dreams of abandonment and a feeling of aloneness in the world. He stated that he was "tired of being a one-of-a-kind freak." Gonzo lamented that he didn't know where he came from or what he truly was. Contradicting all past accounts of Gonzo's youth, it is established that Gonzo has never known his family (or anyone of his species) and feels that he is not just a unique and distinct individual, but also part of a species on the brink of extinction. Gonzo is contacted by aliens channeling his breakfast cereal, and a pair of Cosmic Fish soon reveal to him that he is, in fact, an alien from outer space. It is later revealed that many "zotons" ago Gonzo was lost, and his family has been looking for him. His alien family has been trying to contact him for some time by placing the message "R U There" all over Earth. After they make contact with Gonzo, they make plans (via a sandwich) to rejoin with their long-lost brother and take him home. They arrive at Cape Doom in their giant spaceship (guided by an egg-like light beacon). The aliens displayed the same general physical characteristics as Gonzo's (such as the nostril-less crook-shaped nose and blue/purple fur). They are a musical culture, and their "most ceremonious of ceremonies" includes blowing the honoree out of a cannon. Gonzo is ecstatic to discover what he is, and considers going with them; however in the end he realizes his true home is on Earth with his Muppet family. In the years immediatly following the release of Muppets from Space, most merchandise labeled Gonzo as an alien (his vechile in Muppet Race Mania is a spaceship) but that direction with the character was soon abandoned and Gonzo was reverted back to being labeled a "whatever". Ref: http://muppet.wikia.com/wiki/Gonzo#What_is_Gonzo.3F

There was an episode on The Muppet Show where kermit asked Gonzo "What exactly are you Gonzo?" to which Gonzo answers "Why, I'm a wierdo-of course." So I have told my children that is what Gonzo is- He is a wierdo.