It is shown that the recently proposed preon model which provides a unified origin of the diverse mass scales and an explanation of family replication as well as of inter-family mass-hierarchy, naturally possesses a Peccei-Quinn (PQ) symmetry whose spontaneous breaking leads to an automatic invisible axion. Existence of the PQ-symmetry is simply a consequence of supersymmetry and the requirement of minimality in the field-content and interactions, which proposes that the lagrangian should possess only those terms which are dictated by the gauge principle and no others. In addition to the axion, the model also generates two superlight Goldstone bosons and their superpartners all of which are cosmologically safe.