We present a supersymmetric model of fermion masses, based on a non-Ab
elian family symmetry and the Froggatt-Nielsen mechanism, that can acc
ount for the solar and atmospheric neutrino problems via quasi-degener
ate neutrinos. The model predicts that the ratio of neutrino mass squa
red splittings Delta m(12)(2) /Delta m(23)(2) is of order m(s)(2)/m(b)
(2) and the angles theta(12) similar to m(d)/m(s) and theta(23) simila
r to 1, which are of the desired orders of magnitude. We discuss the i
mplications of the flavor structure of the neutrino sector on superpar
ticle masses and mixing angles. (C) 1998 Elsevier Science B.V.