The Two-Headed Muppet Monster is a character that appeared on Fanfare and The Mike Douglas Show. This creature should not be confused with the Two Headed Monster from Sesame Street.
On Fanfare, the monster chatted with Al Hirt and sang "You're Just in Love" (with slightly altered lyrics such as "I keep tossing in his sleep at night - and what's more, I've lost his appetite!").
One of the monster's heads made an appearance as a cow in The Muppets on Puppets.
In an appearance on The Merv Griffin Show in 1983, Frank Oz recalls that the monster was his first speaking role with the Muppets.