Bajaga i Instruktori followed their debut album with Sa druge strane jastuka ("On the Other Side of the Pillow") in 1985, considered by many to be one of the greatest pop-rock albums in Yugoslav-Serbian history. Bajaga i Instruktori rose to mega-fame that year, and virtually every song on the album became an instant hit. The group received a song-of-the-year award for the mega-hit "Zažmuri", and the album also featured the now-classic songs "220 u voltima", "Ti se ljubiš", "Dvadeseti vek", "Dobro jutro, džezeri", "Vidi šta sam ti uradio od pesme, mama" (a cover version of Melanie Safka's "What Have They Done To My Song, Ma?"), "Francuska ljubavna revolucija" and the popular title track "Sa druge strane jastuka", among several other songs.
Bajaga i Instruktori moved in a slightly different direction with the release of their third album Jahači magle(Fog Riders) released in 1987. The album featured further experimentation with musical genres and presented a technical masterpiece of sound quality and creative output. Again, virtually every song on the album was an instant hit. It featured the classic Bajaga rock numbers "300 na sat", "Samo nam je ljubav potrebna" and "Kao ne zna da je gotivim", as well as the popular song "442 do Beograda" and another rock-jazz fusion, "Red i mir". As with "Sa druge strane jastuka", Bajaga and Dejan Cukić shared vocal duties – particularly apparent in the hit song "Bam, bam, bam".
After Jahači magle, Cukić left Bajaga i Instruktori and started his successful solo career. Bajaga i Instruktori released a new album titled Prodavnica tajni ("Shop of Secrets") in 1988. Inspired in part by Bajaga i Instruktori’s tour of Soviet Union, Prodavnica tajni had a more melancholy mood than the previous three albums, but included several hit songs. Among those was the folkish-sounding "Plavi safir", "Gore-dole", "Verujem, ne verujem", "Ruski voz", "Tišina", "Godine prolaze" and "Život je nekad siv, nekad žut".
The group returned with the release of Neka svemir čuje nemir ("May the Universe Hear the Unrest") in 1989, a compilation of new songs and live recordings. The album's title track "Neka svemir čuje nemir" and the pop number "Na vrhovima prstiju" became two of the band's big hits.
Bajaga i Instruktori followed up with Od bižuterije do ćilibara ("From Tinsel to Amber") in 1997, a self-recorded full album. This release was only moderately successful and can be best remembered for the song "Iza nas". The diminished technical quality and seemingly bland, uninspired and almost depressive sound pointed to what many fans feared was a decline in the band’s inspiration and creativity.
In a fitting move for the ‘new’ political times in Serbia, Bajaga agreed to compose the soundtrack for the feature film Profesionalac ("The Professional") in 2003. This included the hit song "Pada vlada". The band followed up by releasing a compilation of past hits that had a relation to the city of Belgrade, titled Ruža vetrova Beograda ("Belgrade Wind Rose") in 2004. The compilation included two new songs: "Novosti" and the title track "Ruža vetrova", as well as an urban remix of the same track. Both versions of the title track were moderately successful.
Bajaga i Instruktori released a new studio album titled Šou počinje u ponoć ("The Show Begins at Midnight") in 2005. The album featured nine new songs and a diverse mix of musical genres. Potential hits included the title track "Šou počinje u ponoć", as well as the songs "Otrov", "Padaj kišo, keve ti" and "Kap po kap". Bebi Dol made a guest appearance on the album in the songs "Bademi i so" and "Pesma slobode". The release was expected to far better than Zmaj od Noćaja. A tour followed the album and a release of a live DVD recorded in the Belgrade Arena.
People from Belgrade feel a particular attachment to Bajaga’s material of the 1980s and early 1990s, as his music was thought in large part to symbolize that city. Bajaga i Instruktori’s recent concert appearances in the former Yugoslavia (including performances in Slovenia,Croatia and Bosnia and Herzegovina ) as well as in the remainder of Europe, Canada and the United States, have proven that the group still enjoys an extensive fan base.
Momčilo Bajagić "Bajaga" is widely (and rightfully) accepted to be the leading figure in the group. He is regarded as an outstanding lyricist and composer, having also written many songs for the famous pop singer Zdravko Čolić. Respect for Bajaga remains high in Serbia, particularly in upper/intellectual social circles.