We calculate the predictions for lepton flavour violating (LFV) tau and muon decays, $l_j \to l_i \gamma$, $l_j \to 3 l_i$, $\mu-e$ conversion in nuclei and LFV semileptonic tau decays $\tau \to \mu PP$ with $PP= \pi^+\pi^-, \pi^0\pi^0, K^+K^-, K^0 {\bar K}^0$ $\tau \to \mu P$ with $P=\pi^0, \eta, \eta'$ and $\tau \to \mu V$ with $V = \rho^0, \phi$, performing the hadronisation of quark bilinears within the chiral framework. We work within a SUSY-seesaw context where the particle content of the Minimal Supersymmetric Standard Model is extended by three right-handed neutrinos plus their corresponding SUSY partners, and where a seesaw mechanism for neutrino mass generation is implemented. Two different scenarios with either universal or non-universal soft supersymmetry breaking Higgs masses at the gauge coupling unification scale are considered. After comparing the predictions with present experimental bounds and future sensitivities, the most promising processes are particularly emphasised.

7 pages, 9 figures.

Peer reviewed