The detectability of a sinusoidal signal embedded in a masker at the signal frequency can be improved by simultaneously presenting additional maskers in off-frequency regions if the additional maskers and the on-frequency masker component have the same temporal envelope. This effect is commonly referred to as comodulation masking release (CMR). Recently, it was hypothesized that peripheral nonlinear processes such as suppression may play a role in CMR over several octaves when the level of the off-frequency masker component is higher than the level of the on-frequency masker component. The aim of the present study was to test this hypothesis by measuring suppression and CMR within the same subjects for various frequency-level combinations of the off-frequency masker component. Experimental data for normal-hearing listeners show a large overlap between the existence regions for suppression and CMR. Hearing-impaired subjects with a sensorineural hearing loss show, on average, negligible suppression and CMR. The data support the hypothesis that part of the CMR in experiments with large spectral distances and large level differences between the masker components is due to the nonlinear processing at the level of the cochlea.