An important step toward understanding how the brain represents complex natural sounds is to develop accurate models of auditory coding by single neurons. A commonly used model is the linear-nonlinear spectro-temporal receptive field (STRF; LN model). The LN model accounts for many features of auditory tuning, but it cannot account for long-lasting effects of sensory context on sound-evoked activity. Two mechanisms that may support these contextual effects are short-term plasticity (STP) and contrast-dependent gain control (GC), which have inspired expanded versions of the LN model. Both models improve performance over the LN model, but they have never been compared directly. Thus, it is unclear whether they account for distinct processes or describe one phenomenon in different ways. To address this question, we recorded activity of neurons in primary auditory cortex (A1) of awake ferrets during presentation of natural sounds. We then fit models incorporating one nonlinear mechanism (GC or STP) or both (GC+STP) using this single dataset, and measured the correlation between the models’ predictions and the recorded neural activity. Both the STP and GC models performed significantly better than the LN model, but the GC+STP model outperformed both individual models. We also quantified the equivalence of STP and GC model predictions and found only modest similarity. Consistent results were observed for a dataset collected in clean and noisy acoustic contexts. These results establish general methods for evaluating the equivalence of arbitrarily complex encoding models and suggest that the STP and GC models describe complementary processes in the auditory system.