Recent studies have shown a close correspondence between perceptual detection thresholds for sounds in quiet and a measure of neuronal thresholds derived from the stimulus-dependent timing of the first spike of auditory-nerve fibers. In addition, stimulus properties might be encoded by differences in first-spike timing of neurons in the central auditory system. Therefore, the physiological mechanisms underlying first-spike timing are of considerable interest, but are not thoroughly understood. Here, we present a physiological model which accurately explains the observed stimulus dependence of the first-spike latency of auditory-nerve fibers with a minimum number of physiologically plausible parameters. Two of the 5 parameters can be considered constant (at least for the vast majority of fibers), while the other 3 vary in meaningful ways with the fibers' spontaneous discharge rates. The elements of the model and some implications are discussed.