Congenital nystagmus is an involuntary bilateral horizontal oscillation of the eyes that develops soon after birth. In this study, the time constants of each of the components of the neural signal underlying congenital nystagmus were obtained by time series analysis and interpreted by comparison with those of the normal oculomotor system. In the neighbourhood of the fixation position, the system generating the neural signal is approximately linear with 3 degrees of freedom. The shortest time constant was in the range of 7-9 ms and corresponds to a normal saccadic burst signal. The other stable time constant was in the range of 22-70 ms and corresponds to the slide signal. The final time constant characterises the unidentified neural mechanism underlying the unstable drift component of the oscillation cycle and ranges between 31 and 32 ms across waveforms. The characterisation of this unstable time constant poses a challenge for the modelling of both the normal and abnormal oculomotor control system. We tentatively identify the unstable component with the eye position signal supplied to the superior colliculus in the normal eye movement system and explore some of the implications of this hypothesis.