  The lepton flavour violating (LFV) $\tau$ decays $\tau\to (e,\mu)\gamma$ and
$\tau\to 3\mu$ are investigated in the frameworks of the TeV scale type I
see-saw and Higgs Triplet (or type II see-saw) models. Predictions for the
rates of these processes are obtained. The implications of the existing
stringent experimental upper bounds on the $\mu\to e + \gamma$ and $\mu\to 3e$
decay branching ratios for the predictions of the $\tau\to (e,\mu)\gamma$ and
$\tau\to 3\mu$ decay rates are studied in detail. The possibilities to observe
the indicated LFV $\tau$ decays in present and future experiments are analysed.
