Three modifications of a psychoacoustically and physiologically motivated processing model [Dau et al., J. Acoust. Soc. Am. 102 (1997a) 2892-2905] are presented and tested. The modifications aim at simulating sensorineural hearing loss and incorporate a level-dependent peripheral compression whose properties are affected by hearing impairment. Model 1 realizes this difference by introducing for impaired listeners an instantaneous level-dependent expansion prior to the adaptation stage of the model. Model 2 and Model 3 realize a level-dependent compression with time constants of 5 and 15 ms, respectively, for normal hearing and a reduced compression for impaired hearing. In Model 2, the compression occurs after the envelope extraction stage, while in Model 3, envelope extraction follows compression. All models account to a similar extent for the recruitment phenomenon measured with narrow-band stimuli and for forward-masking data of normal-hearing and hearing-impaired subjects using a 20-ms, 2-kHz tone signal and a 1-kHz-wide bandpass noise masker centered at 2 kHz. A clear difference between the different models occurs for the processing of temporally fluctuating stimuli. A modulation-rate-independent increase in modulation-response level for simulating impaired hearing is only predicted by Model 1 while the other two models realize a modulation-rate-dependent increase. Hence, the predictions of Model 2 and Model 3 are in conflict with the results of modulation-matching experiments reported in the literature. It is concluded that key properties of sensorineural hearing loss (altered loudness perception, reduced dynamic range, normal temporal properties but prolonged forward-masking effects) can effectively be modeled by incorporating a fast-acting expansion within the current processing model prior to the nonlinear adaptation stage. Based on these findings, a model of both normal and impaired hearing is proposed which incorporates a fast-acting compressive nonlinearity, representing the cochlear nonlinearity (which is reduced in impaired listeners), followed by an instantaneous expansion and the nonlinear adaptation stage which represent aspects of the retro-cochlear information processing in the auditory system.