When a damped exponential with a half-life of 4-8 ms is repeated every 25-50 ms and used to modulate a sinusoid or a wideband noise, it suppresses the sound quality typically associated with the carrier. When the envelopes of these "damped" sounds are reversed in time, producing "ramped" sounds, a continuous component with the sound quality of the carrier is restored to the perception. This paper presents an experiment that measures the temporal asymmetry revealed by this perceptual contrast. A ramped sinusoid or noise with a given half-life was presented with a damped sinusoid or noise having the same or greater half-life, to determine the damped half-life required to produce a continuous component with the equivalent relative strength in the two sounds. The results with sinusoidal carriers show that the half-life of the damped sound has to be, on average, about five times the half-life of the ramped sound if the tonal component of the two perceptions is to have the same relative strength. The asymmetry for the noise carrier is about half that of the sinusoidal carrier and, again, the damped sound has the greater matching half-life. Several multichannel auditory models based on a gammatone filterbank are used to try to explain the data in terms of traditional leaky integration, but they produce neither sufficient asymmetry nor the correct pattern of asymmetry. A "delta-gamma" theory is then developed to provide a framework for understanding temporal asymmetry in the auditory system. The theory is used to compare the temporal asymmetry produced by several auditory models and to explain when and how they can accommodate the perceptual asymmetry observed in the experiments.