In 1988, he formed his backing band, Spori Ritam Band ("Slow Rhythm Band"). The first lineup of the band featured Dragan Mitrić (keyboards), Vlada Negovanović (a former Doktor Spira i Ljudska Bića and Tunel member, guitar), Safet Petrovac (a former Piloti member, guitar), Slobodan Jurišić (a former Mama Co Co and Točak Band member, drums), and Branko Isaković (a former Bulevar, Suncokret and Idoli member, bass guitar). In 1989, Isaković moved to Kerber, and was replaced by Bata Božanić. This lineup recorded the album "Zajedno" ("Together"). The title track was a cover of The Beatles' song "Come Together". Soon after the album release, Petrovac and Božanić left the band, and Božanić was replaced by former Jugosloveni member Nenad Novaković. In 1991, both Isaković and Petrovac returned to the band. Album "1991" was during the same year. It featured a cover of Bulevar's song "Nestašni dečaci" ("Wild Boys"). At the time, the Yugoslav wars started, and Cukić made a three-year break in his work.