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The transient behavior of thin wires with nonlinear resistive load in the presence of a dielectric half-space is analyzed directly in the time domain. The nonlinear wire problem is formulated by the space-time Hallen integral equation. The effect of a two-media configuration is taken into account via the space-time reflection coefficient appearing within the Green function. The resulting integral equation is handled by the space-time boundary integral equation method. The transient response for the case of a thin wire isolated in free space computed by this direct time-domain approach is compared with results obtained by another method solved using data derived from frequency-domain analysis. Results for various other configurations are also presented.