The firing times of neurons produce a sequence of brief electrical pulses (action potentials) that can be regarded as a stochastic point process. In this report a well-cited model (Smith and Goldberg, 1986) for the firing times of the mammalian peripheral vestibular nerve is used to examine the effect of cumulative vs noncumulative afterhyperpolariztion on the serial dependence among the resultant spike train. A non-renewal point process is indicated at moderate to high firing rates in the case of cumulative afterhyperpolarization. The dependence is Markovian and is a function of the duration of the previous interspike interval. The modelling and biological consequences of this rate dependent serial dependence in the context of neural information processing in the vestibular system ( Linder et al., 2005; Rowe and Neiman, 2012;Sadeghi et al., 2007) and more general neural models (Kostal and Lansky, 2011; Tomar and Kostal, 2021) is explored.