Neutrino Oscillations and the Anomalous Atmospheric Neutrino Flux

We reanalyze the constraints on atmospheric ${\ensuremath{\nu}}_{e}$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ fluxes due to three-neutrino oscillations and investigate the anomalous neutrino fluxes recently observed at Kamiokande. We find that it is difficult to explain the data by ${\ensuremath{\nu}}_{e}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ oscillations alone. We also show that models of three neutrino flavors with neutrino-mass-squared differences of order ${10}^{\ensuremath{-}2}$ ${\mathrm{eV}}^{2}$ can solve both the solar and the atmospheric neutrino problems simultaneously.