There is growing evidence that the dynamics of biological systems that appear to be exponential over short time courses are in some cases better described over the long-term by power-law dynamics. A model of rate adaptation at the synapse between inner hair cells and auditory-nerve (AN) fibers that includes both exponential and power-law dynamics is presented here. Exponentially adapting components with rapid and short-term time constants, which are mainly responsible for shaping onset responses, are followed by two parallel paths with power-law adaptation that provide slowly and rapidly adapting responses. The slowly adapting power-law component significantly improves predictions of the recovery of the AN response after stimulus offset. The faster power-law adaptation is necessary to account for the “additivity” of rate in response to stimuli with amplitude increments. The proposed model is capable of accurately predicting several sets of AN data, including amplitude-modulation transfer functions, long-term adaptation, forward masking, and adaptation to increments and decrements in the amplitude of an ongoing stimulus.