  We analyze the solar and the atmospheric neutrino problems in the context of
three flavour neutrino oscillations. We assume a mass hierarchy in the vacuum
mass eigenvalues $\mu_3^2 \gg \mu_2^2 \geq \mu_1^2$, but make no approximation
regarding the magnitudes of the mixing angles. We find that there are small but
continuous bands in the parameter space where the constraints imposed by the
current measurements of $ \ {}^{71} Ga$, ${}^{37} Cl$ and Kamiokande
experiments are satisfied at $1 \sigma$ level. The allowed parameter space
increases dramatically if the error bars are enlarged to $1.6 \sigma$. The
electron neutrino survival probability has different energy dependence in
different regions of the parameter space. Measurement of the recoil electron
energy spectrum in detectors that use $\nu - e$ scattering may distinguish
between some of the allowed regions of parameter space. Finally we use the
results for the parameter space admitted by the solar neutrinos as an input for
the atmospheric neutrino problem and show that there exists a substantial
region of parameter space in which both problems can be solved.
