Their first recording to be released was the 1980 EP Folk of the 80's. Frontman and songwriter Ivan Doroschuk was the only constant member, while Stefan and Colin Doroschuk as well as Arrobas remained as relatively steady members through the early 1980s. In addition to the Doroschuks, the group has also included numerous additional members and guest or touring performers, many of whom quickly came and left during the first five years. The group's name came about because the brothers, following a self-described principle of 'style before comfort', refused to wear hats during Montreal's cold winters, calling themselves 'the men without hats'. They moved to Montreal as young children when their parents returned to Canada. The Doroschuk brothers, all three of whom are classically trained musicians, were born in Champaign, Illinois while their father, a Canadian, was earning a doctoral degree.

Many years later, Stefan would reuse the Wave 21 name for a country-pop band founded in the late 2010s with his daughters Mary-Lynn and Emmy-Lou. Years earlier, while in high school, Arrobas and the Doroschuk brothers had played together in a short-lived band called Wave 21, along with drummer Igor Krichevsky. Influences on this electronic outfit included Gary Numan, Orchestral Manoeuvres in the Dark (OMD) and Ultravox. In 1980, Doroschuk restarted Men Without Hats, giving the name to a new synthesizer-based group that he formed with Jérémie Arrobas (vocals, keyboards) and his brothers Stefan Doroschuk (bass) and Colin Doroschuk (guitar). Men Without Hats was founded in Montreal in 1977, initially as a punk rock band featuring Ivan Doroschuk (vocals), Pete Seabrooke (guitar), Dave Hill (bass), and John Gurrin (drums).

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