  We study the structures of partition functions of the large $N$ generalized
two-dimensional Yang-Mills theories ($gYM_2$) by recasting the higher Casimirs.
We clarify the appropriate interpretations of them and try to extend the
Cordes-Moore-Ramgoolam's topological string model describing the ordinary
$YM_2$ \cite{CMR} to those describing $gYM_2$. We present the expressions of
the appropriate operators to reproduce the higher Casimir terms in $gYM_2$. The
concept of ''deformed gravitational descendants'' will be introduced for this
purpose.

High Energy Physics - Theory