Neutrino Oscillations and the Anomalous Atmospheric Neutrino Flux

We reanalyze the constraints on atmospheric ${\nu }_e$ and ${\nu }_{\mu }$ 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 ${\nu }_e\leftrightarrow {\nu }_{\mu }$ oscillations alone. We also show that models of three neutrino flavors with neutrino-mass-squared differences of order ${10}^{-2\mathrm{}}$ ${\mathrm{eV}}^2$ can solve both the solar and the atmospheric neutrino problems simultaneously.