Studies of central auditory processing underlying speech-in-noise recognition in aging have mainly concerned the degrading neural representation of speech sound in the auditory brainstem and cortex. Less attention has been paid to the aging-related decline of inhibitory function, which reduces the ability to suppress distraction from irrelevant sensory input. In a response suppression paradigm, young and older adults listened to sequences of three short sounds during MEG recording. The amplitudes of the cortical P30 response and the 40-Hz transient gamma response were compared with age, hearing loss, and speech-in-noise performance. Sensory gating, indicated by the P30 amplitude ratio between the last and the first response, was reduced in older compared to young listeners. Sensory gating was correlated with age in the older adults but not with hearing loss nor with speech-in-noise understanding. The transient gamma response expressed less response suppression. However, the gamma amplitude increased with age and speech-in-noise loss. Comparisons of linear multi-variable modeling showed a stronger brain-behaviour relationship between the gamma amplitude and speech-in-noise performance than between gamma and age or hearing loss. The findings support the hypothesis that aging-related changes in the balance between inhibitory and excitatory neural mechanisms modify the generation of gamma oscillations, which impacts on perceptual binding and consequently on speech-in-noise understanding abilities. In conclusion, speech-in-noise recognition in older age is less affected by central auditory processing at the level of sensation, indicated by sensory gating, but is strongly affected at the level of perceptual organization, indicated by the correlation with the gamma responses.