The author considers nonlinear nonconvex control systems of the form \(x'(t) = f(x(t),u(t))\) where \(u(t)\) belongs to a connected subset \(\Omega\) of a compact metric space. Introducing two families of time-dependent controls, the measurable one and the Lipschitz one, for a given initial value \(x\in \mathbb{R}^n\), the author estimates the distance between the set of solutions generated with measurable controls and the set of solutions generated with \(M\)-Lipschitz controls. He proves that this estimation is of order \(M^{-1/2}\) in the nonconvex case and of order \(M^{-1}\) in some nonlinear convex case.