Incoming sounds are represented in the context of preceding events, and this requires a memory mechanism that integrates information over time. Here, it was demonstrated that response adaptation, the suppression of neural responses due to stimulus repetition, might reflect a computational solution that auditory cortex uses for temporal integration. Adaptation is observed in single‐unit measurements as two‐tone forward masking effects and as stimulus‐specific adaptation (SSA). In non‐invasive observations, the amplitude of the auditory N1m response adapts strongly with stimulus repetition, and it is followed by response recovery (the so‐called mismatch response) to rare deviant events. The current computational simulations described the serial core‐belt‐parabelt structure of auditory cortex, and included synaptic adaptation, the short‐term, activity‐dependent depression of excitatory corticocortical connections. It was found that synaptic adaptation is sufficient for columns to respond selectively to tone pairs and complex tone sequences. These responses were defined as combination sensitive, thus reflecting temporal integration, when a strong response to a stimulus sequence was coupled with weaker responses both to the time‐reversed sequence and to the isolated sequence elements. The temporal complexity of the stimulus seemed to be reflected in the proportion of combination‐sensitive columns across the different regions of the model. Our results suggest that while synaptic adaptation produces facilitation and suppression effects, including SSA and the modulation of the N1m response, its functional significance may actually be in its contribution to temporal integration. This integration seems to benefit from the serial structure of auditory cortex.