The mammalian auditory cortex is necessary for spectral and spatial processing of acoustic stimuli. Most physiological studies of single neurons in the auditory cortex have focused on the onset and sustained portions of evoked responses, but there have been far fewer studies on the relationship between onset and offset responses. In the current study, we compared spectral and spatial tuning of onset and offset responses of neurons in primary auditory cortex (A1) and the caudolateral (CL) belt area of awake macaque monkeys. Several different metrics were used to determine the relationship between onset and offset response profiles in both frequency and space domains. In the frequency domain, a substantial proportion of neurons in A1 and CL displayed highly dissimilar best stimuli for onset- and offset-evoked responses, although even for these neurons, there was usually a large overlap in the range of frequencies that elicited onset, and offset responses and distributions of tuning overlap metrics were mostly unimodal. In the spatial domain, the vast majority of neurons displayed very similar best locations for onset- and offset-evoked responses, along with unimodal distributions of all tuning overlap metrics considered. Finally, for both spectral and spatial tuning, a slightly larger fraction of neurons in A1 displayed nonoverlapping onset and offset response profiles, relative to CL, which supports hierarchical differences in the processing of sounds in the two areas. However, these differences are small compared with differences in proportions of simple cells (low overlap) and complex cells (high overlap) in primary and secondary visual areas.NEW & NOTEWORTHY In the current study, we examine the relationship between the tuning of neural responses evoked by the onset and offset of acoustic stimuli in the primary auditory cortex, as well as a higher-order auditory area-the caudolateral belt field-in awake rhesus macaques. In these areas, the relationship between onset and offset response profiles in frequency and space domains formed a continuum, ranging from highly overlapping to highly nonoverlapping.