Founded and led by vocalist, guitarist and principal composer and lyricist Momčilo Bajagić "Bajaga", the group is one of the most notable acts of the Yugoslav rock scene.

[1] The lineup consisted of Stojković on organ, Bajagić on bass guitar, Dragan Đerić "Đera" on drums and Živorad "Žika" Milenković on vocals.

[1] The group disbanded after only one live performance, and disappointed Bajagić decided to give up music, refusing an invitation from Zdravo leader Boban Petrović to join his band.

[1] The album, entitled Pozitivna geografija (Positive Geography), was released at the end of January 1984 and was well received by the audience, bringing numerous hits: "Berlin", "Mali slonovi" ("Little Elephants"), "Poljubi me" ("Kiss Me"), "Limene trube" ("Brass Trumpets"), "Tekila gerila" ("Tequila Guerrilla"), "Marlena", and "Tamara".

[1] For the opening of the song "Tamara" Bajagić, on the suggestion of musician Dušan Mihajlović "Spira", decided to include a recording of a girl saying several lines in Russian language.

[3] The album featured the anti-drug song "Znam čoveka" ("I Know a Man"), dedicated to Dragan Đerić "Đera", Bajagić's former bandmate from Ofi and Glogov Kolac.

[1] At the beginning of 1985 Bajaga i Instruktori recorded the album Sa druge strane jastuka (On the Other Side of the Pillow), co-produced by Kornelije Kovač and Saša Habić.

[6] Sa druge strane jastuka was the band's first album to feature Milenković as an author: he co-wrote the song "Francuska ljubavna revolucija" ("French Love Revolution") with Bajagić.

[1] The album brought hits "220 u voltima" ("220 Volt"), "Vidi šta sam ti uradio od pesme, mama" (a Serbo-Croatian cover of the Melanie Safka song "Look What They've Done to My Song Ma"), "Ti se ljubiš (Na tako dobar način)" ("You Kiss (In a great Manner)"), "Dvadeseti vek" ("Twentieth Century"), and ballads "Dobro jutro, džezeri" ("Good Morning, Jazzers"), "Sa druge strane jastuka" and "Zažmuri" ("Close Your Eyes").

[8] In March 1985 Bajaga i Instruktori presented their new songs to the Zagreb audience in Kulušić club, as a part of the BG-ZG: Bolje vas našli (Belgrade-Zagreb: Happy to Be Here) action.

[9] After the end of the tour, the band made a break once again, during which Bajagić travelled to Thailand, and Cukić released his first solo album, Spori ritam (Slow Rhythm).

[9] The album marked a slight stylistic change in the band's sound: the songs were simpler, without brass instruments and numerous guest musicians, frequent on the band's previous releases, based on acoustic guitars and keyboards, and the songs "Plavi safir" ("Blue Sapphire"), "Vesela pesma", "Život je nekad siv – nekad žut" and "Ruski voz" featured folk music elements.

[17] In 1991 the band released the EP Četiri godišnja doba (Four Seasons), which featured the songs "Uspavanka" ("Lullaby"), "Buđenje ranog proleća" ("Awakening of the Early Spring"), "Dobro jutro" ("Good Morning"), and "U koži krokodila" ("In Crocodile Skin").

[9] The anti-war ballad "Golubica" ("Dove") featured Aleksandra and Kristina Kovač, Tanja Jovićević of Oktobar 1864 and Marija Mihajlović on backing vocals.

[9] After the album release, Bajagić started to perform alone in the clubs abroad, with the audience usually consisting of young people who emigrated from former Yugoslav republics.

The recordings featured members of the old town music band Legende, in the hit song "Moji drugovi" ("My Friends"), Dragan Jovanović "Krle" of Generacija 5 on acoustic guitar, Sava Latinović on tarabuka, and Aleksandra and Kristina Kovač on backing vocals.

[2] It featured two previously unrecorded songs: "Slovenačka reč" ("A Word in Slovenian"), recorded live and sung by Milenković, featuring music from the band's old song "Idem (Kao da ne idem, a idem)" and Slovenian language lyrics written by journalist Sonja Javorik, and "Pesna protiv maleri" ("A Song against Bad Luck"), recorded in studio for the theatre play Kutrite mali hrčki (Poor Little Hamsters) by Skopje Drama Theatre and sung by Bajagić, featuring Macedonian language lyrics.

[28] During the same year they performed in the United States, in Boston, New York City (in Cooper Union Great Hall), Montreal, San Francisco, Los Angeles and Chicago,[29] and director Miloš Jovanović recorded a documentary about the band entitled Muzika na struju.

The album, which ended up selling around 30,000 copies according to frontman Bajaga himself,[32] was announced by the singles "Ako treba da je kraj" ("If It Should Be the End")[33] and "Vreme" ("Time"),[34] and featured a new version of "Bežiš od mene, ljubavi" and a version of the song "Od sumraka do svitanja" ("From Dusk till Dawn"),[35] written by Bajagić and originally recorded by pop singer Karolina Gočeva in 2005.

The book featured lyrics Bajagić had written for Bajaga i Instruktori and his solo albums, as well as for other artists, with accompanying texts by playwright and academic Dušan Kovačević, Belgrade University professor Aleksandar Jerkov and journalist Peca Popović.

[40] On 26 June 2013 the band held a concert at Belgrade Kalemegdan Fortress in front of 30,000 spectators, as a part of Daljina, dim i prašina promotional tour.

The concert featured Shark, Snakes and Planes, Eva Braun and Bombaj Štampa as the opening bands, and actor and drummer Srđan Todorović, YU Grupa bass guitarist Žika Jelić and Plavi Orkestar frontman Saša Lošić "Loša" as special guests.

[46] The album featured the song "Kad mesec prospe rekom srebra sjaj" ("When the Moon Spills Silver Glow over the River").

[46] In August 2018 Bajaga i Instruktori concert on the Days of Beer festival in Karlovac, Croatia was cancelled, after protests from the veterans of Croatian War of Independence.

The compositions were released on the soundtrack album Nije loše biti čovek, featuring singer and actress Lena Kovačević and actor Gordan Kičić on vocals.

[53] In 2022 Croatia Records and PGP-RTS released the double live album Koncert za rock grupu, orkestar i zbor – Sava Centar 2019.

Cvetković, who was a forming member of the band, stated that he decided to retire from performing due to the fact that he had recently turned 70, while Macura's decision was influenced by the desire to dedicate himself to his new business and spend more time with his family.

Just like Vladimir Velmar-Janković, who climbed to the Kalemegdan hill to reveal a deep analysis of men from these lands, just like Dušan Radović, who placed his nest at the top of Beograđanka to foster, watch over and defend the spirit under these skies, just like Momo Kapor, who collected the golden dust of the city while fooling around – Bajaga, in his own time, left originally poetic and colorful image of an emotional pot which is constantly boiling.

In 2015 Serbian jazz singer Lena Kovačević released a tribute album to Bajaga i Instruktori, entitled Džezeri (Jazzers), featuring covers of ten songs by the band.

[59] The song "Tišina" ("Silence") was, with altered lyrics and entitled "Alkoholičarka" ("Alcoholic Girl"), covered by Serbian punk rock band Trula Koalicija on their 1992 album Plakao sam kad je pala Sekuritatea (I Cried When the Securitate Had Fallen).