In this paper, we prove that the Hodge-components of Hochschild homology of a reduced affine hypersurface are given by torsion modules of Kaehler differentials. Using results of T. Goodwillie, J.-L. Loday and U. Vetter we prove a new vanishing result for the Hodge-components of cyclic homology of affine hypersurfaces and give an explicit computation of these Hodge-components of cyclic homology in the case of an hypersurface defined by a quasi-homogeneous polynomial.