  The main dynamical mechanisms of the reaction $\pi^-p \rightarrow a^0_0
(980)n \rightarrow \pi^0\eta n$ at high energies, currently investigated at
Serpukhov and Brookhaven, are considered in detail. It is shown that the
observed forward peak in its differential cross section can be explained within
the framework of the Regge pole model only by the conspiring $\rho_2$ Regge
pole exchange. The tentative estimates of the absolute $\pi^-p \rightarrow
a^0_0(980)n \rightarrow \pi^0\eta n$ reaction cross section at $P_{lab}^{\pi^-}
= 18$ GeV/c are obtained: $\sigma\approx200$ nb and, in the forward direction,
$d\sigma/dt\approx940$ nb/GeV$^2$. The contribution of the one pion exchange,
which is forbidden by $G$-parity and which can rise owing to the
$f^0_0(980)-a^0_0(980)$ mixing, is also estimate. A role of the Regge cuts in
the non-flip helicity amplitude is briefly examined and a conclusion is made
that the contributions of the cuts have to be inessential in comparison with
the conspiring $\rho_2$ Regge pole exchange.
