The band was formed by Draško "Drakula" Nikodijević, original member and former bass player Igra Staklenih Perli and young and prospective female drummer Snow White.
The theater show never happened but the band added young female bass player Maya Papović and started touring.
During the 80s many musicians passed through the band: former Igra Staklenih Perli Vojkan Rakić on guitar, Thrile and Griša on bass and Borko Petrović on drums.
After relocating in late 80's to New York, Nikodijević released a conceptual album there under the name "White Rabbit Cult" in 1999 and it was more industrial sample based music.
White Rabbit Band has risen again in September 2013 with Nikodijević on bass and vocals, former Igra Staklenih Perli TNG, Električni Orgazam and Partibrejkers member Vlada Funtek on drums and guitarist Andrija Babović.