In the paper small C¹-perturbations of differential equations are considered. The concepts of a weakly hyperbolic set K and a sheet Υ{hooked} for a system of ordinary differential equation are introduced. Lipschitz property is not assumed to hold. It is shown that if the perturbation is small enough, then there is a continuous mapping h: Υ{hooked} → Υ{hooked}^Y, where Υ{hooked}^Y is a sheet of the perturbed system.