Forward masking growth functions were measured for pure-tone maskers and signals at 2 and 6 kHz as a function of the silent interval between the masker and signal. The inclusion of conditions involving short signals and short masker-signal intervals ensured that a wide range of signal thresholds were recorded. A consistent pattern was seen across all the results. When the signal level was below about 35 dB SPL the growth of masking was shallow, so that signal threshold increased at a much slower rate than masker level. When the signal level exceeded this value, the masking function steepened, approaching unity (linear growth) at the highest masker and signal levels. The results are inconsistent with an explanation for forward-masking growth in terms of saturating neural adaptation. Instead the data are well described by a model incorporating a simulation of the basilar-membrane response at characteristic frequency (which is almost linear at low levels and compressive at higher levels) followed by a sliding intensity integrator or temporal window. Taken together with previous results, the findings suggest that the principle nonlinearity in temporal masking may be the basilar membrane response function, and that subsequent to this the auditory system behaves as if it were linear in the intensity domain.