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We introduce a general parametric form of the current-voltage characteristic of space-charge-limited currents (SCLC) in a trap-free material with nonlinear velocity-field (v-F) dependence. An exact solution is obtained for two important v-F models describing the gradual transition from the Mott–Gurney law to the regime of drift-velocity saturation. In particular, we discuss the effect of negative differential mobility on the current-voltage characteristic of SCLC in the high-field region. The theory shows a good agreement with experimental data for low-temperature pulsed SCLC in GaAs.