Stimulus-specific adaptation (SSA) is the reduction in responses to frequent stimuli (standards) that does not generalize to rare stimuli (deviants). We investigated the contribution of inhibition in auditory cortex to SSA using two-photon targeted cell-attached recordings and optogenetic manipulations in male mice. We characterized the responses of parvalbumin (PV)-, somatostatin (SST)-, and vasoactive intestinal polypeptide (VIP)-expressing interneurons of layer 2/3, and of serotonin receptor 5HT3a-expressing interneurons of layer 1. All populations showed early-onset SSA. Unexpectedly, the PV, SST, and VIP populations exhibited a substantial late component of evoked activity, often stronger for standard than for deviant stimuli. Optogenetic suppression of PV neurons facilitated pyramidal neuron responses substantially more (approximately ×10) for deviants than for standards. VIP suppression decreased responses of putative PV neurons, specifically for standard but not for deviant stimuli. Thus, the inhibitory network does not generate cortical SSA, but powerfully controls its expression by differentially affecting the responses to deviants and to standards.SIGNIFICANCE STATEMENT Stimulus-specific adaptation (SSA) reflects the growing complexity of auditory processing along the ascending auditory system. In the presence of SSA, neuronal responses depend not only on the stimulus itself but also on the history of stimulation. Strong SSA in the fast, ascending auditory pathway first occurs in cortex. Here we studied the role of the cortical inhibitory network in shaping SSA, showing that while cortical inhibition does not generate SSA, it powerfully controls its expression. We deduce that the cortical network contributes in crucial ways to the properties of SSA.