A linear, phenomenological theory of the nonlocal dielectric response is extended to the non-linear case. For small external electric fields, we give solutions within a perturbation approach. Results, obtained by molecular dynamics computer simulations for the non-linear response of water are in very good agreement with the theory predictions. The results are applied to the calculation of the electrostatic potential of ions in solution. For the electric field strengths, for which the perturbation theory is still applicable, there are only minor differences with respect to the linear case. A fitting procedure to the simulation data, which covers a wider range of electric fields shows, however, that at larger fields the non-linear effects may change the results considerably, relative to those obtained on the basis of the linear response approximation. We discuss a generalization of the nonlocal electrostatic approach to the calculation of solvation energies, which takes into account non-linear effects.