The circumstances under which Unicef was formed, as well as the later stages, are somewhat hazy. What is clear is that the founding members were Tino and Jonza. Tino played guitar, Fagey played bass and Jonza (who, at that time, used the name Danny Kaye) sang, and came up with the name for the band. This lineup probably played only one gig. The identity of the drummer is unclear, but among the people who played in Unicef before the later, better known lineup, were Eno, Pitkä, Rusina, Antsu, Hannu and Hippo.

Unicef either broke up or was put on hold when Tino and Jonza travelled to Portugal. At the time they returned to Finland Lama had broken up, so Tino, Jonza and Rane Raitsikka (ex-Lama) decided to get together. T.B. Widow (ex-Widows) joined to play bass and possibly Eno (ex-Lama) on drums. After a few legendary gigs Johanna wanted to release a single from the band. Jusa (also ex-Lama) was then asked to join in. The single Käkimassaa was released in 1983, and featured Tino and Jonza on vocals, Rane on guitar and bass, and Jusa on drums.

How the band came to an end is also a bit hazy. The lineup was constantly changing, and as Tino, Jonza and some other people from the Helsinki scene moved abroad, the story of Unicef was also over. Only one single and the legend remained.

After Unicef Rane Raitsikka played in Smack, and later moved to United States. Jusa has worked in the Helsinki music scene, and played drums in some minor bands. Jonza and Tino are no longer alive.