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Carrier sweep‐out rates from GaAs/AlGaAs multiple quantum wells have been measured as a function of excitation level on picosecond time scales at different values of applied electric field. A minimum rate of ∼20 ps was observed under resonant tunneling conditions at low generated carrier densities. At higher excitation levels, the effects of space charge build‐up were found to significantly alter the transient nonlinear optical response due to changes in the time constant associated with vertical carrier transport.