With Cochlear Implants (CIs), interleaving two pulse trains modulated respectively at 80 and 120 Hz produces a neural distortion response (NDR) at 40 Hz in the cortical EEG response. Understanding how this NDR is generated may help diagnose the auditory nerve (AN) physiological status of CI users. We investigated two phenomenological models of the AN, one that included refractoriness and spike-rate adaptation (“Brochier2022”), and one that additionally included facilitation and accommodation (“Joshi2017”). The two pulse trains were separated by an inter-pulse interval (IPI) ranging from 0 to 1000 µs. We quantified the summed neural activity at 40 Hz. Both models created an NDR. At IPIs below 400 µs and in the Joshi2017 model, this was driven by facilitation between pulses, while at IPIs above 400 µs (and all IPIs for the Brochier2022 model), refractoriness was the main generation mechanism. Neither model predicted the reduction in NDR at longer IPIs seen in humans, but a modified version (with a faster release from refractoriness) of the Brochier2022 model could. The phase of the NDR was better predicted by refractoriness generation than facilitation. This suggests NDRs may already be present at the level of the AN and reflect fundamental temporal-interaction mechanisms.