at a rate of one out of [Formula omitted] tau decays?

We present in a full analytic form the partial widths for the lepton flavour violating decays [Formula omitted] and [Formula omitted], with [Formula omitted], 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 [Formula omitted], we retain full dependence on [Formula omitted], the momenta and masses of external particles, and we determine the branching ratios in the physical limit [Formula omitted]. We show that the claim presented in Pham (Eur Phys J C8:513, 1999) that the [Formula omitted] branching ratios could be as large as [Formula omitted], as a consequence of keeping the [Formula omitted] dependence, is flawed. We find rates of order [Formula omitted], even smaller than those obtained in the zero momentum limit, as the latter prediction contains an unphysical logarithmic enhancement.