  Using the auxiliary field representation of the simplicial chiral models on a
(d-1)-dimensional simplex, the simplicial chiral models are generalized through
replacing the term Tr$(AA^{\d})$ in the Lagrangian of these models by an
arbitrary class function of $AA^{\d}$; $V(AA^{\d})$. This is the same method
used in defining the generalized two-dimensional Yang-Mills theories (gYM_2)
from ordinary YM_2. We call these models, the ``generalized simplicial chiral
models''. Using the results of the one-link integral over a U(N) matrix, the
large-N saddle-point equations for eigenvalue density function $\ro (z)$ in the
weak ($\b >\b_c$) and strong ($\b <\b_c$) regions are computed. In d=2, where
the model is in some sense related to the gYM_2 theory, the saddle-point
equations are solved for $\ro (z)$ in the two regions, and the explicit value
of critical point $\b_c$ is calculated for $V(B)$=Tr$B^n$ $(B=AA^{\d})$. For
$V(B$)=Tr$B^2$,Tr$B^3$, and Tr$B^4$, the critical behaviour of the model at d=2
is studied, and by calculating the internal energy, it is shown that these
models have a third order phase transition.
