Considerable debate surrounds claims for early evidence of music in the archaeological record. Researchers universally accept the existence of complex musical instruments as an indication of fully modern behaviour and advanced symbolic communication but, owing to the scarcity of finds, the archaeological record of the evolution and spread of music remains incomplete. Although arguments have been made for Neanderthal musical traditions and the presence of musical instruments in Middle Palaeolithic assemblages, concrete evidence to support these claims is lacking. Here we report the discovery of bone and ivory flutes from the early Aurignacian period of southwestern Germany. These finds demonstrate the presence of a well-established musical tradition at the time when modern humans colonized Europe, more than 35,000 calendar years ago. Other than the caves of the Swabian Jura, the earliest secure archaeological evidence for music comes from sites in France and Austria and post-date 30,000 years ago.