Abstract: The object of the present paper is to study weakly symmetric Riemannian manifolds.Among others it is shown that a conformally flat weakly symmetric Riemannian manifold is of hyper quasi-constant curvature which generalizes the notion of quasi-constant curvature and also such a manifold is a quasi-Einstein manifold.Finally several examples of weakly symmetric manifolds of both zero and non-zero scalar curvature are obtained.