Optokinetic nystagmus (OKN) is a reflexive eye movement with a characteristic pattern of alternating fast and slow phases (resembling a noisy sawtooth), but with significant variation in the timing and amplitude of its components. We attempt to predict the sequence of OKN fast and slow phases by embedding them in state space and forming local approximations to the resulting trajectories. There is significant predictability only in the sequence of fast phase starting and ending positions. This is presumably related to the desire of the oculomotor system to aim the eyes at a location in space where something important might be expected to appear, leading to a partially deterministic rule for generating the end points of the fast phases.