abstract: For a polarized algebraic manifold (M,L), the existence of a Kaehler metric of constant scalar curvature implies the K- semistabilty of (M,L) by the works of Chen-Tian and Donaldson. It is also known that the existence implies the asymptotic Chow-stability for (M,L) relative to an algebraic torus. By looking at these two stabilities in examples, we shall discuss how they differ.