Żywiołak was founded in Warsaw in 2006 by the multi-instrumentalists Robert Jaworski (born 3rd May, 1975 in Turek) and Robert Wasilewski. Both of them had previously played in well-known folk groups – Jaworski with Kapela Ze Wsi Warszawa and Wasilewski with Open Folk. The band was later joined by drummer Maciej Łabudzki and vocalists Anna Piotrowska and Izabela Byra.
In December 2005, the group won the audience award at the Mikołajki Folkowe International Folk Music Festival in Lublin. In May of the next year, they won the Grand Prix Award of the President of Polish Radio at Warsaw's Nowa Tradycja festival. The band’s style, a combination of folk and garage rock, has enabled the band to perform not only on folk but also on rock stages. In December 2006, Żywiołak won the Młode Wilki – Rebelia competition, which was organized at the Warsaw venue Stodoła, besting L.Stadt and Muchy, amongst others.
During the Dialogue of Four Cultures Festival in Łódź, Żywiołak performed without Łabudzki, who was substituted by Maciej Dymek. In the beginning of 2008, the band qualified for the elimination round of the Eurovision song contest with the song Noc Kupały, but eventually wasn't able to perform at the finale concert because they were disqualified for breaking the rules of the competition – they performed the submitted song at a concert before they were supposed to.
In 2007, the group released their debut EP Muzyka psychodelicznej świtezianki, which contains the tracks Oko dybuka and Świdryga i midryga to a poem by Bolesław Leśmian, Pogaństwo, and two versions of Psychoteka. This EP was a foretaste of the album Nowa ex-tradycja (2008). This album broadened the boundaries of rock and showed that combining this genre with folk can sound modern and original. The acoustic folk instruments harmonize with the sounds of the fuzzy guitar, the hard sound of the bass guitar and the strong percussion rhythms (this is best exemplified by Żywiołak, which was exceptionally sung by Jaworski, and Oko dybuka). This harmonizing gives the music a dark atmosphere, and sounds trance-like, almost psychedelic. The album includes traditional songs such as Oj a na Jana Kupała and Oj ti, Pietrie, Pietrie, and the lyrics of Psychoteka are based on Leśmian’s Karczma. Jaworski’s poetic lyrics sound like folk tales, but he also sometimes refers to Polish history (such as in Żywiołak) and assesses the contemporary longing for power (for instance, in Pogaństwo, which was already featured on the EP).