  The simplest unified extension of the Minimal Supersymmetric Standard Model
with bi-linear R-parity violation naturally predicts a hierarchical neutrino
mass spectrum, suitable to explain atmospheric and solar neutrino fluxes. We
study whether the individual violation of the lepton numbers L_{e,mu,tau} in
the charged sector can lead to measurable rates for BR(mu->e gamma)and
$BR(tau-> mu gamma). We find that some of the R-parity violating terms that are
compatible with the observed atmospheric neutrino oscillations could lead to
rates for mu->e gamma measurable in projected experiments. However, the Delta
m^2_{12} obtained for those parameters is too high to be compatible with the
solar neutrino data, excluding therefore the possibility of having measurable
rates for mu->e gamma in the model.
