The small C¹ perturbations of differential equations are studied. The concepts of a weakly hyperbolic set K and a leaf ϒ are introduced for a system of ordinary differential equations. The Lipschitz condition is not supposed. It is shown that, if the perturbation is small enough, then there exists a continuous mapping h : ϒ → ϒ^Y, where ϒ^Y is a leaf of the perturbed system.