The simplest unified extension of the Minimal Supersymmetric Standard Model with bi-linear R--Parity violation provides a predictive scheme for neutrino masses which can account for the observed atmospheric and solar neutrino anomalies in terms of bi-maximal neutrino mixing. The maximality of the atmospheric mixing angle arises dynamically, by minimizing the scalar potential, while the solar neutrino problem can be accounted for either by large or by small mixing oscillations. One neutrino picks up mass by mixing with neutralinos, while the degeneracy and masslessness of the other two is lifted only by loop corrections. Despite the smallness of neutrino masses R-parity violation is observable at present and future high-energy colliders, providing an unambiguous cross-check of the model.

5 pages, final version published in Phys. Rev. D61, 2000, 071703(R)