Nonlinear optical materials, such as transparent conductive oxides, have recently drawn a lot of attention when being integrated into metasurfaces and allowing full-optical control of the surface response. Although several methods for modeling the nonlinear materials have been proposed in the literature, most of them have the limitations on being non-dispersive and of instantaneous response. In this paper, we present a straightforward integration of an extended Drude-Lorentz model that captures the local intensity response of nonlinear materials while being dispersive and allowing for inertial response via a low-pass filtering process. This method is integrated into standard finite difference time-domain (FDTD) implementation of Maxwell’s equations and the auxiliary differential equations approach of the Drude-Lorentz model is extended via local intensity-dependent parameters. A numerical demonstration shows the response for a thin film of nonlinear material, where the parameters across the sample are time-varying with respect to the local intensity of the fields. Therefore, showing a direct feedback of the field profile to the nonlinear response of the material, which is critical when incorporating such films in resonating meta-atoms.