  We compute the lepton flavour violating couplings of Higgs bosons in the
Minimal Supersymmetric Standard Model, and show that they can induce the decays
(h,H,A) --> mu tau at non-negligible rates, for large tan(beta) and sizeable
smuon-stau mixing. We also discuss the prospects for detecting such decays at
LHC and other colliders, as well as the correlation with other flavour
violating processes, such as tau --> mu gamma and tau --> 3 mu.
