  We analyze the spectrum and mixing among neutrinos in the minimal
supersymmetric standard model with explicit breaking of R parity. It is shown
that ({\em i}) the mixing among neutrinos is naturally large and ({\em ii}) the
non zero neutrino mass is constrained to be $\leq 10^{-5}$ eV from arguments
based on baryogenesis. Thus vacuum oscillations of neutrinos in this model may
offer a solution of the solar neutrino problem. The allowed space of the
supersymmetric parameters consistent with this solution is determined.
