Two simple models are examined in order to explain the observation that a portion of the binaural-evoked response is less than the sum of monaural-evoked responses in human and animal subjects. The sum of monaural responses minus the binaural response is called the binaural difference (BD). Each model acts on binaural input signals and applies a single memoryless nonlinearity. One model (IE) applies a rectifying nonlinearity to the difference of input signals, while the other (EE) applies a compressive nonlinearity to the sum of input signals. These models are suggested by properties of inhibitory-excitatory (IE) and excitatory-excitatory (EE) neurons of the auditory brainstem. Parameters can be found that enable each model to produce a ratio of BD to summed monaural response which is invariant with input stimulus level. The IE model, but not the EE model, has a BD whose level is linearly related to input stimulus level.