  The evaluation, systematic analysis and numerical study of the semileptonic
$\tau$-lepton decays with two mesons in the final state has been made in the
frame of the standard model extended by right handed neutrinos. In the
analysis, heavy-neutrino nondecoupling effects, finite quark masses, quark and
meson mixings, finite widths of vector mesons, chiral symmetry breakings in
vector-meson--pseudoscalar-meson vertices and effective
Higgs-boson--pseudoscalar-meson couplings have been included. Numerical
estimates reveal that the decays $\tau^-\to e^-\pi^-\pi^+$, $\tau^-\to
e^-K^-K^+$ and $\tau^-\to e^-K^0\bar{K}^0$ have branching ratios of the order
of $10^{-6}$, close to present-day experimental sensitivities.
