An accurate model of auditory nerve fibers (ANFs) would help in improving cochlear implant (CI) functionality. Previous studies have shown that the original Hodgkin-Huxley (1952) model (with kinetics adjusted for mammalian body temperature) 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 long-term accommodation, adaptation and the time-course of relative refractoriness. Recent physiological investigations of spiral ganglion cells have shown the presence of a number of ion channel types not considered in the previous modeling studies, including low-threshold potassium (I(KLT)) channels and hyperpolarization-activated cation (I(h)) channels. In this paper we investigate inclusion of these ion channel types in a stochastic HH model. For single biphasic charge-balanced pulse, an increase in spike threshold was typically produced by inclusion of one or both of these channel types. The addition of I(KLT) increases random threshold fluctuations in the stochastic model, particularly for longer pulse widths. Pulse-train responses were investigated for pulse rates of 200, 800, and 2000 pulse/s. Initial results suggests that both the I(KLT) channels and I(h) channels can produce adaptation in the spike rate. However, the adaptation due to I(KLT) is restricted to higher stimulation rates, whereas the adaptation due to I(h) is observed across all stimulation rates.