Since their foundation in Reykjavík in 1978, the group consisted of Egill Ólafsson (vocals, keyboards) and acoustic guitar, guitarist Þórður Arnason, bassoonist Rúnar Vilbergsson, bassist Tómas Magnús Tómasson and drummer Ásgeir Óskarsson.
On their fourth album, Gæti eins verið... from 1982, the band had switched style completely into playing new wave music.
The acoustic instruments were nearly completely substituted by synthesizers; keyboarder Karl Sighvattson and bassoonist Rúnar Vilbergsson had left the band.
For the band's 30th anniversary in February 2008, all their albums were reissued in a mini-vinyl-box with a CD full of previously unissued tracks and live versions.
In addition, there was a tour through Iceland in early 2008 with the small orchestra Capút; a live CD-DVD was issued in late November 2008 with the title Hinn íslenski Þursaflokkur og Caput.