A new name, a new approach, new possibilities. Oleksandr Dem’yanenko (guitar, domra and mandolin) was invited to play with the group.  In addition to playing solo concerts, HAYDAMAKY were invited to participate in festivals all across Europe, such as the Pohoda Festival (2001, 2002, Trencin Slovakia), the Viljandi Folk, and Parismuusika Festival (2003, Viljandi, Estonia), and Litomerzickyj Korzen (2002, 2003, Litomerz, Czech Republic). 
Still working on their second album, the group released their first video Polissya directed by Victor Pryduvalov. While the Haydamaky album featured such outstanding musicians as Vitaliy Pantsyo (cimbalom) Taras Kompanichenko (kobza), Yevgen Horyslavskyi (trumpet), and Oleksiy Kabanov (lyre), the second album Bohuslav gathered even more of Ukraine's best musicians. In the song Legend (Bohuslav album), one can hear the unique sounds of the bandura played by Roman Hrynkiv, who is world renound for his joint works with Andreas Vollenweider and Al Di Meola. Famous bandura and guitar player Yuriy Fedynskyi came especially from New York to participate in the album’s recording; back-up vocals for the album were performed by an authentic Ukrainian choir, Bozhychi. While working on the album, HAYDAMAKY immersed themselves even deeper into Ukraine’s folk culture in search of ideas, material and texture for the album. The Bohuslav album was released in April 2004.  A few months later, a video was made for the song Bohuslav under the direction of Oles Sanin.