  Lepton-flavour violating processes, such as $\mu \to e\gamma$, are studied in
ordinary (non-SUSY) SU(5) and SUSY SU(5) grand unified theories. First given
are some introductory argument on the mechanism of U.V. divergence cancellation
in flavour changing neutral current processes and on the decoupling of
particles with GUT scale masses . We next see that such general argument is
confirmed by an explicit calculation of the amplitude of $\mu \to e\gamma$ in
ordinary SU(5), which shows that logarithmic divergence really cancels among
diagrams and remaining finite part are suppressed by at least $1/M_{GUT}^2$. In
SUSY SU(5), flavour changing slepton mass-squared term get a logarithmic
correction, as recently claimed. However, when the effect of flavour changing
wave function renormalization is also taken into account such logarithmic
correction turns out to disappear, provided a condition is met among SUSY
breaking soft masses. In SUGRA-inspired SUSY GUT, such condition is not
satisfied. But the remaining logarithmic effect is argued not to be taken as a
prediction of the theory associated with an irrelevant operator. We find that
the log-correction should not exist in models with gauge mediated SUSY
breaking.
