  We study the phenomenology of the e-mu lepton flavour violation (LFV) in a
general two Higgs Doublet Model (2HDM) including the supersymmetric case. We
compute the decay rate expressions of mu -> e gamma, mu -> eee, and mu -> e
conversion in nuclei at two loop level. In particular, it is shown that mu -> e
gamma is generally the most sensitive channel to probe Higgs-mediated LFV. The
correlations among the decay rates of the above processes are also discussed.
