The supersymmetric standard model with softly broken lepton symmetry provides a suitable framework to accommodate the solar and atmospheric neutrino anomalies. This model contains a natural explanation for large mixing and hierarchal masses without fine-tuning the parameters. The neutrino spectrum is particularly constrained in the minimal messenger model (MMM) of gauge mediated SUSY breaking, since all SUSY breaking effects are controlled in the MMM essentially by a single parameter. We study the structure of neutrino masses and mixing both in the MMM and in simple extensions of it in the context of solar and atmospheric neutrino anomalies.

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