We report on the establishing of an exclusive magnetic effect in air-exposed CoxC60 nanocomposites (x > 2) created through self-assembling in the depositing mixture. In order to verify the influence of ambient air on the CoxC60 mixture film, we have studied in detail the film magnetization at rather low temperatures, which provides their ferromagnetic behavior. Tracing the possible exchange bias effect, we distinguished a clear vertical shift of the hysteresis loops recorded for the air-exposed CoxC60 films in the field cooling (FC) regime. The detected vertical shift of the FC loops is caused by an uncompensated magnetic moment M u induced by exchange coupling of the Co spins at the Co/CoO interface. This interface arises due to the oxidation of small Co clusters distributed in a C60-based matrix of self-assembled composite films, which occurs during air exposure. The core-shell structure of the Co/CoO magnetic clusters (about 2-3 nm in size) consisting of a ε-Co core and fcc-CoO shell was confirmed by means of transmission electron microscopy. Established interface magnetism testifies to a composite nanostructure in the CoxC60 mixture film with x > 2 and explains the influence of air exposure on the film structure. The discovered magnetic effect implies a new application potential for cobalt-fullerene composites in sensors and catalysis.