The question of structural stability is one of the most important areas in a present-day theory of differential equations. In this paper, we study small C¹ perturbations of a systems of differential equations. We introduce the concepts of a weakly hyperbolic invariant set K and leaf Y for a system of ordinary differential equations. The Lipschitz condition is not assumed. We show that, if the perturbation is small enough, then there is a continuous mapping h, i.e., K → K^Y, where K^Y is a weakly hyperbolic set of the perturbed equation system. Moreover, we show that h(Y) is a leaf of the perturbed system.