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The nonlinear, spatially-dispersive response of a semiconductor or plasma to large-amplitude time-harmonic electromagnetic fields is obtained by solving the nonlinear transport equation using an harmonic expansion. The conduction response, which is nonlinear and generally spatially and temporally dispersive, is given as a hierarchical set of linear second-order differential equations with non-linear forcing terms. The polarization response is assumed linear. A simple slab example is shown that admits analytical solutions for the nonlinear material response to various orders. As the solution order grows, the nonlinear forcing terms grow in complexity, although the differential equations remain second-order. In the static limit, the two lowest-order solutions are shown to identically satisfy the dc transport equation.