It has been well documented that neurons in the auditory cortex of anaesthetized animals generally display transient responses to acoustic stimulation, and typically respond to a brief stimulus with one or fewer action potentials. The number of action potentials evoked by each stimulus usually does not increase with increasing stimulus duration. Such observations have long puzzled researchers across disciplines and raised serious questions regarding the role of the auditory cortex in encoding ongoing acoustic signals. Contrary to these long-held views, here we show that single neurons in both primary (area A1) and lateral belt areas of the auditory cortex of awake marmoset monkeys (Callithrix jacchus) are capable of firing in a sustained manner over a prolonged period of time, especially when they are driven by their preferred stimuli. In contrast, responses become more transient or phasic when auditory cortex neurons respond to non-preferred stimuli. These findings suggest that when the auditory cortex is stimulated by a sound, a particular population of neurons fire maximally throughout the duration of the sound. Responses of other, less optimally driven neurons fade away quickly after stimulus onset. This results in a selective representation of the sound across both neuronal population and time.