  The combined requirements, of (i) a natural solution to the fermion mass
hierarchy problem and (ii) an explanation of both the atmospheric and solar
neutrino problems, lead to an essentially unique picture of neutrino masses and
mixing angles. The electron and muon neutrinos are quasi-degenerate in mass
with maximal mixing, giving $\nu_e - \nu_{\mu}$ vacuum oscillations. The
overall neutrino mass scale is set by the atmospheric neutrino requirement
$\Delta m^2 \sim 10^{-2}$ eV$^2$, implying a mass for $\nu_e$ and $\nu_{\mu}$
of order 1 eV in models with a natural mass hierarchy, whilst the tau neutrino
is expected to be much lighter than this and only weakly mixed. We present an
explicit example based on the anti-grand unification model of fermion masses.
