  We study the implications of a large nu_mu - nu_tau mixing angle on flavour
changing transitions of quarks and leptons in supersymmetric extensions of the
standard model. Two patterns of supersymmetry breaking are considered, models
with modular invariance and the standard scenario of universal soft breaking
terms at the GUT scale. The analysis is performed for two symmetry groups G x
U(1)_F, with G=SU(5) and G=SU(3)^3, where U(1)_F is a family symmetry. Models
with modular invariance are in agreement with observations only for restricted
scalar quark and gaugino masses, (M_squark^2)/(m_gluino^2) \simeq 7/9 and
m_bino > 350 GeV. A characteristic feature of models with large tan beta and
radiatively induced flavour mixing is a large branching ratio for mu -> e
gamma. For both symmetry groups and for the considered range of supersymmetry
breaking mass parameters we find BR(mu -> e gamma) > 10^(-14).
