If supersymmetry is realized with spontaneous breaking of R-parity, th
ere will be many phenomenological consequences. Here we show that the
masses and mixing angles of the neutrinos lie in the correct range for
the MSW explanation of the solar neutrino problem. At the same time t
he rates for the processes Z0 --> tau + chargino, tau --> mu + Majoron
and mu --> e + Majoron can be close to the present bounds.