We investigated neural coding of sinusoidally modulated tones (sAM and sFM) in the primary auditory cortex (A1) of awake marmoset monkeys, demonstrating that there are systematic cortical representations of embedded temporal features that are based on both average discharge rate and stimulus-synchronized discharge patterns. The rate-representation appears to be coded alongside the stimulus-synchronized discharges, such that the auditory cortex has access to both rate and temporal representations of the stimulus at high and low frequencies, respectively. Furthermore, we showed that individual auditory cortical neurons, as well as populations of neurons, have common features in their responses to both sAM and sFM stimuli. These results may explain the similarities in the perception of sAM and sFM stimuli as well as the different perceptual qualities effected by different modulation frequencies. The main findings include the following. 1) Responses of cortical neurons to sAM and sFM stimuli in awake marmosets were generally much stronger than responses to unmodulated tones. Some neurons responded to sAM or sFM stimuli but not to pure tones. 2) The discharge rate-based modulation transfer function typically had a band-pass shape and was centered at a preferred modulation frequency (rBMF). Population-averaged mean firing rate peaked at 16- to 32-Hz modulation frequency, indicating that the A1 was maximally excited by this frequency range of temporal modulations. 3) Only approximately 60% of recorded units showed statistically significant discharge synchrony to the modulation waveform of sAM or sFM stimuli. The discharge synchrony-based best modulation frequency (tBMF) was typically lower than the rBMF measured from the same neuron. The distribution of rBMF over the population of neurons was approximately one octave higher than the distribution of tBMF. 4) There was a high degree of similarity between cortical responses to sAM and sFM stimuli that was reflected in both discharge rate- or synchrony-based response measures. 5) Inhibition appeared to be a contributing factor in limiting responses at modulation frequencies above the rBMF of a neuron. And 6) neurons with shorter response latencies tended to have higher tBMF and maximum discharge synchrony frequency than those with longer response latencies. rBMF was not significantly correlated with the minimum response latency.