The group formed in Adelaide in 1979, with all the members coming from the Koonibba Mission (near Ceduna, South Australia).
In 1980, together with another Australian aboriginal band, Us Mob, they made a film, Wrong Side of the Road, which detailed the bands touring the central Australian region.
In 1982 their debut EP, From My Eyes, was launched by the then Prime Minister of Australia, Bob Hawke. The same year they toured Australia in support of Peter Tosh. No Fixed Address then became the first Australian Aboriginal band to tour overseas, giving a number of performances in Great Britain.