In 1984, the band released the album Treći svijet, featuring distinctive world music-influenced sound with Rudnek's poetic lyrics inspired by various works of literature, film and comics.

The basis of the band was formed in 1977, when Darko Rundek and Srđan Sacher started the informal group Komuna (Comune), with which they performed occasionally.

[1] One of the two songs, "Moja prva ljubav" ("My First Love"), the lyrics of which were partially inspired by the short story "The Girls in Their Summer Dresses" by Irwin Shaw,[2] soon became a radio hit.

[1] They were noted for their artistic songs and performances, influenced by Rundek's and Sacher's interests – Rundek, who had switched to studies of directing at the Zagreb Academy of Dramatic Art, introduced theatricality, pantomime and theatrical makeup into the band's performances, while Sacher, who was at the time a student of archaeology and ethnology, introduced elements of Yugoslav and foreign ethnic music into the band's new wave sound.

[3] The album brought, alongside "Moja prva ljubav", which went on to become a major hit, slightly mystical and psychedelic songs "Radio", "Mijenjam se" ("I'm Changing"), "Tko je to" ("Who Is That"), "Duhovi" ("Ghosts"), "Crni žbir" ("Black Spy"), "Lice" ("Face") and "60–65."

[3] The album should have featured the song "Radnička klasa odlazi u raj" ("The Working Class Goes to Heaven"), named after the 1971 film by Italian director Elio Petri.

[3] Haustor's work on their second studio album was interrupted when part of the members was drafted to serve their mandatory stints in the Yugoslav People's Army in February 1982.

[3] The band continued their activity at the beginning of 1983, in the lineup featuring Rundek, Sacher, Prica, Gulić, and a new member, guitarist Zoran Zajec.

[3] With former Metak guitarist Željko Brodarić "Jappa" as the producer and with a brass section, the band recorded their second studio album Treći svijet (Third World), releasing it in 1983.

[3] The songs "Neobičan dan" ("Unusual Day"), "Zadnji pogled na Jeršaleim" ("The Last Look at Yerushaláyim"), "Babilonske baklje" ("Torches of Babylon"), "Skriven iza lažnih imena" ("Hidden Behind False Names") and the title track brought a distinctive atmosphere which was novel to Yugoslav rock scene.

[3] Other musicians who took part in the album recording were Jurij Novoselić (of the band Film, alt saxophone and keyboards), Rastko Milošev (of Parni Valjak, guitar), jazz musician Neven Frangeš (keyboards), with female members of the reggae band Naturalna Mistika (Natural Mystique) and actress Anja Šovagović recording backing vocals.

[3] With all the songs written by Rundek, Bolero brought the second major hit in the band's career, the song "Ena", alongside successful "Šejn" ("Shane"), "Šal od svile" ("Silk Scarf"), "Ja želim" ("I Wish"), "TV Man", "Sejmeni" ("Seimeni") and "Take the Money and Run", the latter featuring elements of rap music.

[3] For the promotional tour, the band was rejoined by Gulić, Prica and Santro, with addition of bass guitarist Mario Barišin (formerly of Trobecove Krušne Peći), keyboardist Alen Bjelinski (formerly of Aerodrom) and trumpeter Igor Pavlica.

[3] The album Tajni grad (Secret City) was recorded with two new members, bass guitarist Marino Pelajić (formerly of Film) and keyboardist Julije Rejić.

[3] The album was well-received by music critics and the public, with the songs "Ula ulala", "Bi mogo da mogu" ("I Could if I Could"), "Uzalud pitaš" ("You Are Asking in Vain"), "Samo na čas" and "Uhode" ("Stalkers") becoming the audience's favorites.

[3] In 1990, while in the midst of the recording of their fifth album, with the working title Dovitljivi mali čudaci (Quick-Witted Little Weirdos), the band suddenly ended their activity.

[3] After Haustor disbanded, Rundek moved with his family to Paris,[3] starting a highly successful career of a singer-songwriter with the release of his 1996 album Apokalipso (Apocalypse).

[3] In 1986, Prica formed the free jazz band Cul-de-Sac (French for Dead End Street) with guitarist Dragan Pajić "Pajo".

[3] In addition to working with Cul-de-Sac, Prica also performed with the avant-garde band Pink Noise Quartet, recording their 1999 self-titled album with them.

[3] In 2000, Pajić moved back to Zagreb, where he continued the activity of Cul-de-Sac, adding Orkestar za ubrzanu evoluciju (Orchestra for the Accelerated Evolution) to the band's name.

[3] Rundek, Pavlica, Neven Jurić, Andreja Košavić (vocal, trumpet), Miro Manojlović (vibraphone) and other musicians performed with the band on different occasions.

[3] At the end of 1995, Rundek returned to Zagreb from Paris, holding a series of well-received concerts, with 10,000 visitors in total attending the performances.

[3] The good reception of the performances led to Haustor reuniting for a concert on the 1996 Zagreb gori (Zagreb's Burning) festival, in the lineup featuring Darko Rundek, Srđan Sacher, Zoran Zajec, Damir Prica, Nikola Santro and Igor Pavlica, with Boris Leiner and Ozren Štiglić performing as guests.

[10] The lyrics of sixteen songs by the band, thirteen authored by Rundek, two authored by Sacher and one co-authored by Rundek and Sacher, were featured in Petar Janjatović's book Pesme bratstva, detinjstva & potomstva: Antologija ex YU rok poezije 1967 - 2007 (Songs of Brotherhood, Childhood & Offspring: Anthology of Ex YU Rock Poetry 1967 – 2007).