  We present a supersymmetric model of fermion masses, based on a non-Abelian
family symmetry and the Froggatt-Nielsen mechanism, that can account for the
solar and atmospheric neutrino problems via quasi-degenerate neutrinos. The
model predicts that the ratio of neutrino mass squared splittings \Delta
m^2_{12} / \Delta m^2_{23} is of order m_s^2/m_b^2, and the angles \theta_{12}
\sim m_d/m_s and \theta_{23} \sim 1, which are of the desired orders of
magnitude. We discuss the implications of the flavor structure of the neutrino
sector on superparticle masses and mixing angles.
