The group began in September 1967 with the name Ambition of Music, playing a fairly typical though creative blend of hippie rock. By 1968 the group had merged with a local evangelical brass band to add a more jazz-styled free form of trumpets, trombones, and bassoon to the proceedings. By 1970, the now seven-piece group was renamed Annexus Quam and toured much of Germany as well as playing several concerts in Japan (including a couple days at the Osaka World Fair). In September of that year they recorded material for their first album. Osmose, with its elaborate multi-foldout cover of variable images, became one of the early records on the legendary Ohr label and was released toward the end of the year.

The group played several jazz festivals over the next couple years, and after some lineup changes and personnel exits, they went back into the studio as a five-piece in May 1972 to record the album Beziehungen, released by Ohr later that year. Whereas the debut record threw in many different styles, from psychedelic rock to jazz to strange chanting, by Beziehungen the group had honed themselves into a formidable free jazz improvisational group, the rhythmic rock trappings left far behind. Little is known about the group after this, though they never released any more albums.