In this article we prove, for a differentiable vector field or a diffeomorphism on a smooth manifold, that the set of points such that the semitrajectories issuing from them approach a particular semitrajectory at a given exponential rate, constitute a differentiable submanif old, provided the differential of the flow has a certain similar behavior on that trajectory. (See Theorem 1 below, for a precise statement). In particular, the stable manifold theorem for hyperbolic sets ([3], [6, XI]) follows as a corollary. Although we only consider the Crease, the same methods, which are essentially classical ([2, Ch. XIII]), could be applied to obtain higher differentiability properties. Since I have not seen in the literature this type of results for points which are neither equilibrium nor periodic points, and on account of [6, XI-8], I thought that their publication might not be entirely devoid of interest. 1* Terminology and notation are standard. If X is a differentiable vector field on a smooth manifold M, will always denote the corresponding flow, and φt the diffeomorphism x —> φ(x, t), xeM, te R. For brevity, we shall sometimes write x(t) or y(t) instead of φ(x, t) or φ(y, t) respectively.