### Abstract:

We consider the MSSM with see-saw mechanism of neutrino mass generation and soft SUSY breaking with flavour-universal boundary conditions at the GUT scale, in which the lepton flavour violating (LFV) decays µ → epsilon + gamma, tau → µ + gamma, etc., are predicted with rates that can be within the reach of present and planned experiments. These predictions depend critically on the matrix of neutrino Yukawa couplings Yv which can be expressed in terms of the light and heavy right-handed (RH) neutrino masses, neutrino mixing matrix UPMNS, and an orthogonal matrix R. We investigate the effects of Majorana CP-violation phases in UPMNS, and of the RG running of light neutrino masses and mixing angles from MZ to the RH Majorana neutrino mass scale MR, on the predictions for the rates of LFV decays µ → epsilon + gamma, tau → µ+gamma and tau → epsilon+gamma. Results for neutrino mass spectrum with normal hierarchy, values of the lightest v-mass in the range 0 ≤ m1 ≤ 0.30 eV, and quasi-degenerate heavy RH Majorana neutrinos in the cases of R = 1 and complex matrix R are presented. We find that the effects of the Majorana CP-violation phases and of the RG evolution of neutrino mixing parameters can change by few orders of magnitude the predicted rates of the LFV decays µ → epsilon+gamma and tau → epsilon + gamma. The impact of these effects on the tau→µ+gamma decay rate is typically smaller and only possible for m1 >∼ 0.10 eV. If the RG running effects are negligible, in a large region of soft SUSY breaking parameter space the ratio of the branching ratios of the µ → epsilon + gamma and tau → epsilon + gamma (tau → µ + gamma) decays is entirely determined in the case of R ~= 1 by the values of the neutrino mixing parameters at MZ.