  The LFV charged lepton decays mu to e + gamma, tau to e + gamma and tau to mu
+ gamma and thermal leptogenesis are analysed in the MSSM with see-saw
mechanism of neutrino mass generation and soft SUSY breaking with universal
boundary conditions. The case of hierarchical heavy Majorana neutrino mass
spectrum, M_1 << M_2 << M_3, is investigated. Leptogenesis requires M_1 > 10^9
GeV. Considering the natural range of values of the heaviest right-handed
Majorana neutrino mass, M_3 > 5*10^{13} GeV, and assuming that the soft SUSY
breaking universal gaugino and/or scalar masses have values in the range of few
100 GeV, we derive the combined constraints, which the existing stringent upper
limit on the mu to e + gamma decay rate and the requirement of successful
thermal leptogenesis impose on the neutrino Yukawa couplings, heavy Majorana
neutrino masses and SUSY parameters. Results for the three possible types of
light neutrino mass spectrum -- normal and inverted hierarchical and
quasi-degenerate -- are obtained.
