  Motivated by effective low energy models of string origin, we discuss the
neutrino masses and mixing within the context of the Minimal Supersymmetric
Standard Model supplemented by a U(1) anomalous family symmetry and additional
Higgs singlet fields charged under this extra U(1). In particular, we interpret
the solar and atmospheric neutrino data assuming that there are only three
left-handed neutrinos which acquire Majorana masses via a lepton number
violating dimension-five operator. We derive the general form of the charged
lepton and neutrino mass matrices when two different pairs of singlet Higgs
fields develop non--zero vacuum expectation values and show how the resulting
neutrino textures are related to approximate lepton flavor symmetries. We
perform a numerical analysis for one particular case and obtain solutions for
masses and mixing angles, consistent with experimental data.
