Many theories of cerebellar motor learning propose that complex spikes (CS) provide essential error signals for learning and modulate parallel fiber inputs that generate simple spikes (SS). These theories, however, do not satisfactorily specify what modality is represented by CS or how information is conveyed by the ultra-low CS firing rate (1 Hz). To further examine the function of CS and the relationship between CS and SS in the cerebellum, CS and SS were recorded in the ventral paraflocculus (VPFL) of awake monkeys during ocular following responses (OFR). In addition, a new statistical method using a generalized linear model of firing probability based on a binomial distribution of the spike count was developed for analysis of the ultra-low CS firing rate. The results of the present study showed that the spatial coordinates of CS were aligned with those of SS and the speed-tuning properties of CS and SS were more linear for eye movement than retinal slip velocity, indicating that CS contain a motor component in addition to the sensory component identified in previous studies. The generalized linear model to reproduce firing probability confirmed these results, demonstrating that CS conveyed high-frequency information with its ultra-low firing frequency and conveyed both sensory and motor information. Although the temporal patterns of the CS were similar to those of the SS when the sign was reversed and magnitude was amplified approximately 50 times, the velocity/acceleration coefficient ratio of the eye movement model, an aspect of the CS temporal firing profile, was less than that of the SS, suggesting that CS were more sensory in nature than SS. A cross-correlation analysis of SS that are triggered by CS revealed that short-term modulation, that is, the brief pause in SS caused by CS, does not account for the reciprocal modulation of SS and CS. The results also showed that three major aspects of the CS and SS individual cell firing characteristics were negatively correlated on a cell-to-cell basis: the preferred direction of stimulus motion, the mean percent change in firing rate induced by upward stimulus motion, and patterns of temporal firing probability. These results suggest that CS may contribute to long-term interactions between parallel and climbing fiber inputs, such as long-term depression and/or potentiation.