  The asymmetries between the spectra of leading and nonleading charmed mesons
measured in $\Sigma^-A$ interactions at $p_L$= 340 GeV/c in the WA89 experiment
are described in the framework of Quark-Gluon String Model. There are two
versions of the model under consideration: one of them includes the sea charm
quark-antiquark pairs and the other one does not. It's shown that the
asymmetries between $D^-$ and $D^+$-meson spectra and between $D_s^-$ and
$D^+_s$- meson spectra can be fitted by QGSM curves obtained with the same
parameters as charm asymmetry in $\pi^-A$ experiments described in previous
studies. The QGSM results are compared with the calculations in the
next-to-leading approximation of perturbative QCD approach carried out by the
other authors.
