Many anaesthetics commonly used in auditory research severely depress cortical responses, particularly in the supragranular layers of the primary auditory cortex and in non-primary areas. This is particularly true when stimuli other than simple tones are presented. Although awake preparations allow better preservation of the neuronal responses, there is an inherent limitation to this approach whenever the physiological data need to be combined with histological reconstruction or anatomical tracing. Here we tested the efficacy of an opiate-based anaesthetic regime to study physiological responses in the primary auditory cortex and middle lateral belt area. Adult marmosets were anaesthetized using a combination of sufentanil (8 μg/kg/h, i.v.) and N2O (70%). Unit activity was recorded throughout the cortical layers, in response to auditory stimuli presented binaurally. Stimuli consisted of a battery of tones presented at different intensities, as well as two marmoset calls (‘Tsik’ and ‘Twitter’). In addition to robust monotonic and non-monotonic responses to tones, we found that the neuronal activity reflected various aspects of the calls, including ‘on’ and ‘off’ components, and temporal fluctuations. Both phasic and tonic activities, as well as excitatory and inhibitory components, were observed. Furthermore, a late component (100–250 ms post-offset) was apparent. Our results indicate that the sufentanil/N2O combination allows better preservation of response patterns in both the core and belt auditory cortex, in comparison with anaesthetics usually employed in auditory physiology. This anaesthetic regime holds promise in enabling the physiological study of complex auditory responses in acute preparations, combined with detailed anatomical and histological investigation.