  We study the phenomenology of the mu-tau and e-tau lepton flavour violation
(LFV) in a general two Higgs Doublet Model (2HDM) including the supersymmetric
case. We consider several LFV decay modes of the charged fermion tau, namely
tau-> l_jgamma, tau->l_j l_k l_k and tau-> l_jeta. The predictions and the
correlations among the rates of the above processes are computed. In
particular, it is shown that tau->l_jgamma processes are the most sensitive
channels to Higgs-mediated LFV specially if the splitting among the neutral
Higgs bosons masses is not below the 10% level.
