  The hadroproduction of $D_s$ mesons is discussed within the framework of the
modified Quark-Gluon String model (QGSM) taking into account the decays of
corresponding $S$--wave resonances. A description of the existing experimental
data on inclusive spectra of $D_s$ - mesons production in $\pi p$ - collision
and asymmetry of leading ($D_s^-$) and nonleading ($D_s^+$) mesons in $\Sigma^-
p$-- interaction is obtained. The predictions for cross sections and
leading/nonleading asymmetry in $\pi p$ - and $\Sigma^- p$-- collision for
different initial momenta are also given.
