A number of masking phenomena can be modeled in terms of a linear auditory filter bank followed by a temporal integrator and a simple decision device based on the signal-to-masker ratio. Other aspects require the inclusion of a nonlinearity following linear filtering. The present article concentrates on aspects of non-simultaneous, or "temporal", masking that cannot be explained by either modeling approach. A more realistic nonlinear model of cochlear processing is explored, and it is shown that most aspects of temporal masking can be accounted for with this model, in conjunction with a linear temporal integrator (temporal window) and the simple decision criterion. An earlier version of the model with a static nonlinearity following linear filtering can account for "on-frequency" nonlinearities in masking such as the growth of forward masking, the effects of forward masker duration, and the nonlinear additivity of forward and backward masking. The new model can account, in addition, for frequency-dependent nonlinearities in masking such as the upward spread of forward masking and certain aspects of two-tone suppression.