tau -> mu mu mu at a rate of one out of 10^14 tau decays?

We present in a full analytic form the partial widths for the lepton flavour violating decays mu +/--> e +/- e+e- and tau +/--> l +/- l '+l '-, with l,l '=mu,e, mediated by neutrino oscillations in the one-loop diagrams. Compared to the first result by Petcov (Sov J Nucl Phys 25:340, 1977), obtained in the zero momentum limit PMUCH LESS-THANm nu MUCH LESS-THANMW, we retain full dependence on P, the momenta and masses of external particles, and we determine the branching ratios in the physical limit m nu MUCH LESS-THANPMUCH LESS-THANMW. We show that the claim presented in Pham (Eur Phys J C8:513, 1999) that the tau -> ll ' l ' branching ratios could be as large as 10(-14), as a consequence of keeping the P dependence, is flawed. We find rates of order 10(-55), even smaller than those obtained in the zero momentum limit, as the latter prediction contains an unphysical logarithmic enhancement.