A self-diffeomorphism of (n+m)-space with a fixed hyperbolic point at the origin was considered. The existence of a nontransversal homoclinic point is assumed. It has been proved that when the stable and unstable manifolds are tangent in a certain way, a neighborhood of the homoclinic point may contain stable periodic points, but at least one of the characteristic exponents for such points tends to zero with increasing the period. f is supposed to be a self diffeomorphism of (n + m)-space. W ^s(0), W ^u(0) denote the stable and unstable manifolds of the point 0. It is proved that the neighborhood U may contain a countable set of stable periodic points, but at least one of the characteristic exponents for such points tends to zero with increasing the period.