Because the oscillatory eye movements of congenital nystagmus vary from cycle to cycle, there is no clear relationship between the waveform produced and the underlying abnormality of the ocular motor system. We consider the durations of successive cycles of nystagmus which could be (1) completely determined by the lengths of the previous cycles, (2) completely independent of the lengths of the previous cycles or (3) a mixture of the two. The behaviour of a deterministic system can be characterised in terms of a collection of (unstable) oscillations, referred to as periodic orbits, which make up the system. By using a recently developed technique for identifying periodic orbits in noisy data, we find evidence for periodic orbits in nystagmus waveforms, eliminating the possibility that each cycle is independent of the previous cycles. The technique also enables us to identify the waveforms which correspond to the deterministic behaviour of the ocular motor system. These waveforms pose a challenge to our understanding of the ocular motor system because none of the current extensions to models of the normal behaviour of the ocular motor system can explain the range of identified waveforms. © 2002 Elsevier Science Ltd. All rights reserved.