There are at least three bands with this name:

1. Named after Cold War spies, not small animals, The Moles were an Australian pop band led by Richard Davies (later of the one-off project Cardinal). They were formed in the late 1980s and broke up in the early 1990s, having released the album Untune the Sky and several singles. Davies later revived the band name for what was actually a solo project, Instinct.

2. The Original 1960s band The Moles were Simon Dupree & The Big Sound under another name. They were formed as The Big Sound in Portsmouth as a dance band. They then emerged as The Moles in 1968; they released "We Are The Moles Part 1/Part 2". They reinvented themselves again a few years later as the progressive-rock band Gentle Giant.

3. An internet-based musical collaboration between fans of The Residents, who operated between 1999 and 2005. They produced a very limited edition boxed album called Worm Pizza as a 30th anniversary present, which proved so popular it was reissued in a reduced form.
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