How the brain processes temporal information embedded in sounds is a core question in auditory research. This article synthesizes recent studies from our laboratory regarding neural representations of time-varying signals in auditory cortex and thalamus in awake marmoset monkeys. Findings from these studies show that 1) the primary auditory cortex (A1) uses a temporal representation to encode slowly varying acoustic signals and a firing rate-based representation to encode rapidly changing acoustic signals, 2) the dual temporal-rate representation in A1 represent a progressive transformation from the auditory thalamus, 3) firing rate-based representations in the form of a monotonic rate-code are also found to encode slow temporal repetitions in the range of acoustic flutter in A1 and more prevalently in the cortical fields rostral to A1 in the core region of the marmoset auditory cortex, suggesting further temporal-to-rate transformations in higher cortical areas. These findings indicate that the auditory cortex forms internal representations of temporal characteristic structures. We suggest that such transformations are necessary for the auditory cortex to perform a wide range of functions including sound segmentation, object processing and multi-sensory integration.