Auditory object perception requires binding of elementary features of complex stimuli. Synchronization of high‐frequency oscillation in neural networks has been proposed as an effective alternative to binding via hard‐wired connections because binding in an oscillatory network can be dynamically adjusted to the ever‐changing sensory environment. Previously, we demonstrated in young adults that gamma oscillations are critical for sensory integration and found that they were affected by concurrent noise. Here, we aimed to support the hypothesis that stimulus evoked auditory 40‐Hz responses are a component of thalamocortical gamma oscillations and examined whether this oscillatory system may become less effective in aging. In young and older adults, we recorded neuromagnetic 40‐Hz oscillations, elicited by monaural amplitude‐modulated sound. Comparing responses in quiet and under contralateral masking with multitalker babble noise revealed two functionally distinct components of auditory 40‐Hz responses. The first component followed changes in the auditory input with high fidelity and was of similar amplitude in young and older adults. The second, significantly smaller in older adults, showed a 200‐ms interval of amplitude and phase rebound and was strongly attenuated by contralateral noise. The amplitude of the second component was correlated with behavioral speech‐in‐noise performance. Concurrent noise also reduced the P2 wave of auditory evoked responses at 200‐ms latency, but not the earlier N1 wave. P2 modulation was reduced in older adults. The results support the model of sensory binding through thalamocortical gamma oscillations. Limitation of neural resources for this process in older adults may contribute to their speech‐in‐noise understanding deficits.