Responses to auditory stimuli are often strongly influenced by recent stimulus history. For example, in a paradigm called forward suppression, brief sounds can suppress the perception of, and the neural responses to, a subsequent sound, with the magnitude of this suppression depending on both the spectral and temporal distances between the sounds. As a step towards understanding the mechanisms that generate these adaptive representations in awake animals, we quantitatively characterize responses to two-tone sequences in the auditory cortex of waking mice. We find that cortical responses in a forward suppression paradigm are more diverse in waking mice than previously appreciated, that these responses vary between cells with different firing characteristics and waveform shapes, but that the variability in these responses is not substantially related to cortical depth or columnar location. Moreover, responses to the first tone in the sequence are often not linearly related to the suppression of the second tone response, suggesting that spike-frequency adaptation of cortical cells is not a large contributor to forward suppression or its variability. Instead, we use a simple multilayered model to show that cell-to-cell differences in the balance of intracortical inhibition and excitation will naturally produce such a diversity of forward interactions. We propose that diverse inhibitory connectivity allows the cortex to encode spectro-temporally fluctuating stimuli in multiple parallel ways.NEW & NOTEWORTHY Behavioral and neural responses to auditory stimuli are profoundly influenced by recent sounds, yet how this occurs is not known. Here, the authors show in the auditory cortex of awake mice that the quality of history-dependent effects is diverse and related to cell type, response latency, firing rates, and receptive field bandwidth. In a cortical model, differences in excitatory-inhibitory balance can produce this diversity, providing the cortex with multiple ways of representing temporally complex information.