  The observed alteration of the S-wave $\pi^0\pi^0$ mass spectrum in the
reaction $\pi^-p\to\pi^0\pi^0n$ with increasing $-t$, i.e., the disappearance
of a dip and the appearance of a peak in the region of the $f_0(980)$ resonance
as $-t$ increases, is explained by the contribution of the $\pi^-p\to
f_0(980)n$ reaction amplitude with the quantum numbers of the $a_1$ Regge pole
in the $t$ channel. It is very interesting that nontrivial evidence for the
$a_1$ exchange mechanism in the reaction $\pi^-p\to \pi^0\pi^0n$ follows for
the first time from the experiment on an unpolarized target. The explanation of
the GAMS results suggested by us is compared with that reported previously. Two
ways of experimentally testing these explanations are pointed out.
