Large mixing and large hierarchy between neutrinos with Abelian flavor symmetries

The experimental data on atmospheric and solar neutrinos suggest that there is near-maximal mixing between nu(mu) and nu(tau) but that their masses ar e hierarchically separated. In models of Abelian horizontal symmetries, mix ing of O(1) generically implies that the corresponding masses are of the sa me order of magnitude. We describe two new mechanisms by which a large hier archy between strongly mixed neutrinos can be achieved in this framework. F irst, a discrete Abelian symmetry can give the desired result in three ways : mass enhancement, mixing enhancement and mass suppression. Second, holomo rphic zeros can give mass suppression.