The aim of this study was to attempt to distinguish between neural adaptation and persistence (or temporal integration) as possible explanations of forward masking. Thresholds were measured for a sinusoidal signal as a function of signal duration for conditions where the delay between the masker offset and the signal offset (the offset-offset interval) was fixed. The masker was a 200-ms broadband noise, presented at a spectrum level of 40 dB (re: 20 μPa), and the signal was a 4-kHz sinusoid, gated with 2-ms ramps. The offset-offset interval was fixed at various durations between 4 and 102 ms and signal thresholds were measured for a range of signal durations at each interval. A substantial decrease in thresholds was observed with increasing duration for signal durations up to about 20 ms. At short offset-offset intervals, the amount of temporal integration exceeded that normally found in quiet. The results were simulated using models of temporal integration (the temporal-window model) and adaptation. For both models, the inclusion of a peripheral nonlinearity, similar to that observed physiologically in studies of the basilar membrane, was essential in producing a good fit to the data. Both models were about equally successful in accounting for the present data. However, the temporal-window model provided a somewhat better account of similar data from a simultaneous-masking experiment, using the same parameters. This suggests that the linear, time-invariant properties of the temporal-window approach are appropriate for modeling forward masking. Overall the results confirm that forward masking can be described in terms of peripheral nonlinearity followed by linear temporal integration at higher levels in the auditory system. However, the difference in predictions between the adaptation and integration models is relatively small, meaning that influence of adaptation cannot be ruled out.