Lepton Flavour Violating Decays of Supersymmetric Higgs Bosons

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.