  The instanton--anti-instanton pair induced asymptotics of perturbation theory
expansion for the cross section of electron--positron pair annihilation to
hadrons and hadronic width of $\tau$-lepton was found. For $N_f = N_c$ the
nonperturbative instanton contribution is finite and may be calculated without
phenomenological input. The instanton induced peturbative asymptotics was shown
to be enhanced as $(n+10)!$ and in the intermediate region $n<15$ may exceed
the renormalon contribution. Unfortunately, the analysis of $\sim 1/n$
corrections shows that for $n \sim 10$ the obtained asymptotic expressions are
at best only the order of magnitude estimate. The asymptotic series for $R_{e^+
e^- \rightarrow hadrons}$ , though obtained formally for $N_f =N_c$, is valid
up to energies $\sim 15$Gev. The instanton--anti-instanton pair nonperturbative
contribution to $R_{\tau \rightarrow hadrons}$ blows up. On the one hand, this
means that instantons could not be considered {\it ab--initio} at such
energies. On the other hand, this result casts a strong doubt upon the
possibility to determine the $\alpha_s$ from the $\tau$--lepton width.
