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A previous theory [M. Ershov etal, Appl. Phys. Lett. 67, 3147 (1995)] for studying the distribution of nonuniform fields in multiple-quantum-well photodetectors under an ac voltage is generalized to include nonadiabatic space-charge-field effects. From numerical results calculated by the generalized theory, it is found that field-domain effects are only important at high temperatures or high voltages, where both injection and sequential-tunneling currents are expected to be large. On the other hand, field-domain effects become negligible at low temperatures and low voltages, but nonadiabatic effects included in this extended theory are enhanced for small sequential-tunneling currents. The time duration for nonadiabatic effects is determined by the quantum capacitance. By using the generalized theory, a differential capacitance is calculated for a non-steady state, and a negative conduction current is predicted under a positive voltage in this case due to charge accumulation around the collecting contact.