Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to recorded jerk CN waveforms, and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system. This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses. © Springer Science + Business Media, LLC 2006.