The representation of rapid acoustic transients by the auditory cortex is a fundamental issue that is still unresolved. Auditory cortical neurons have been shown to be limited in their stimulus-synchronized responses, yet the perceptual performances of humans and animals in discriminating temporal variations in complex sounds are better than what existing neurophysiological data would predict. This study investigated the neural representation of temporally asymmetric stimuli in the primary auditory cortex of awake marmoset monkeys. The stimuli, ramped and damped sinusoids, were systematically manipulated (by means of half-life of the exponential envelope) within a cortical neuron's presumed temporal integration window. The main findings of this study are as follows: 1) temporal asymmetry in ramped and damped sinusoids with a short period (25 ms) was clearly reflected by average discharge rate but not necessarily by temporal discharge patterns of auditory cortical neurons. There was considerable response specificity to these stimuli such that some neurons were strongly responsive to a ramped sinusoid but almost completely unresponsive to its damped counterpart or vice versa. Of 181 neurons studied, 140 (77%) showed significant response asymmetry in at least one of the tested half-life values of the exponential envelope. Forty-six neurons showed significant response asymmetry over all half-lives tested. Sustained firing, commonly observed under awake conditions, contributed to greater response asymmetry than that of onset responses in many neurons. 2) A greater proportion of the neurons (32/46) that exhibited significant overall response asymmetry showed stronger responses to the ramped sinusoids than to the damped sinusoids, possibly contributing to the difference in the perceived loudness between these two classes of sounds. 3) The asymmetry preference of a neuron to ramped or damped sinusoids did not appear to be correlated with its characteristic frequency or minimum response latency, suggesting that this is a general phenomenon that exists across populations of cortical neurons. Moreover, the intensity of the stimuli did not have significant effects on the measure of the asymmetry preference based on discharge rate. 4) A population measure of response preference, based on discharge rate, of cortical neurons to the temporally asymmetric stimuli was qualitatively similar to the performance of human listeners in discriminating ramped versus damped sinusoids at different half-life values. These findings suggest that rapid acoustic transients embedded in complex sounds can be represented by discharge rates of cortical neurons instead of or in the absence of stimulus-synchronized discharges.