  In this paper, we consider an obstruction to asymptotic Chow-semistability of
a polarized Kaehler algebraic manifold. Even when a linear algebraic group of
positive dimension acts nontrivially and holomorphically on a polarized Kaehler
algebraic manifold with constant scalar curvature, the vanishing of the
obstruction allows us to generalize Donaldson's construction of approximate
solutions for equations of balanced metrics.
