A general mathematical approach was proposed to study phenomenological models of the inner-hair-cell and auditory-nerve (AN) synapse complex. Two models (Meddis, J. Acoust. Soc. Am. 79(3), 702–711 (1986); Westerman and Smith, J. Acoust. Soc. Am. 83(6), 2266–2276 (1988)) were studied using this unified approach. The responses of both models to a constant-intensity stimulus were described mathematically, and the relationship between model parameters and response characteristics was investigated. The mathematical descriptions of the two models were essentially equivalent despite their structural differences. This analytical approach was used to study the effects of adaptation characteristics on model parameters and of model parameters on adaptation characteristics. The results provided insights into these models and the underlying biophysical processing. This analytical method was also used to study offset adaptation, and it was found that the offset adaptation of both models was limited by the models’ structures. A modified version of the synapse model, which has the same onset adaptation but improved offset adaptation, is proposed here. This modified synapse model produces more physiologically realistic offset adaptation and also enhances the modulation gain of model AN fiber responses, consistent with AN physiology.