The Zimmer Twins, Rick and Leif, are two aging British rock stars who are scheduled to perform on The Muppet Show in "Kermit's Story," the first in Roger Langridge's four-issue run of The Muppet Show Comic Book.
When Scooter cancels their number in order to get the homesick Kermit in front of an audience, Rick, the more lucid of the two, physically intimidates the go-fer; after all, the easily bewildered Leif (who doesn't realize they've left their nursing home) has been looking forward to the gig all week.
The Zimmer Twins are eventually allowed to (literally) crash Kermit's Koozebane sketch, landing a spaceship that was supposed to have housed the Poobs on, and consequently flattening, the Male and Female Koozebanian Creatures. Kermit predicts that this act will set off an intergalactic war.
The Zimmer Twins are a reference to Rolling Stones bandmates Mick Jagger and Keith Richards, popularly known as "Mick and Keef".