[en] We construct an invisible axion model which naturally explains the smallness of Dirac neutrino masses by generating the neutrino masses at the two-loop level. This model also provides a qualitative explanation for the fermion mass hierarchy m_t>>m_b, m_τ>>m_ν. The implications of a possible 17 keV neutrino are discussed. In particular a 17 keV heavy neutrino can have a cosmologically safe fast decay through ν_heavy→ν_light+axion. (orig.)