An accurate model of auditory nerve fibers (ANFs) may assist in developing improved cochlear implant (CI) stimulation strategies. Previous studies have shown that the original Hodgkin-Huxley (HH) model may be better at describing nodes of Ranvier in ANFs than models for other mammalian axon types. However, the HH model is still unable to explain a number of phenomena observed in auditory nerve responses to CI stimulation such as adaptation to high-rate stimulation and the time course of relative refractoriness. Recent physiological investigations of ANFs have shown the presence of a number of ion channel types not considered in the previous modeling studies, including low-threshold potassium (KLT) channels and hyperpolarization-activated cation (HCN) channels. In this paper, we investigate inclusion of these ion channel types in a stochastic HH model of a single node of Ranvier. Simulation results for pulse trains with rates of 200, 800, and 2000 pulse/s suggests that both the KLT channels and HCN channels can produce adaptation in the spike rate. However, the adaptation due to KLT is restricted to higher stimulation rates, whereas the adaptation due to HCN is observed across all stimulation rates. Additionally, using pulse pairs it was found that KLT increased both the absolute and the relative refractory periods. HCN on its own increased just the relative refractory period, but produced a synergistic increase in the absolute refractory period when combined with KLT. Together these results argue strongly for the need to consider HCN and KLT channels when studying CI stimulation of ANFs.