Motor disorders frequently contain a rhythmic component, but the associated oscillations are not usually precisely periodic. This lack of strict periodicity can make it difficult to identify the effects of experimental manipulations on the oscillation. In this report, we describe the application of a numerical technique for identifying fixed points of a nonlinear map to the recovery of underlying periodicities of the eye movement disorder of nystagmus. The technique is illustrated by application to two different types of nystagmus. In addition we use a local analysis of the behaviour at the fixed points to distinguish between different bifurcations in the two examples with changes in gaze angle. We conclude that the technique reveals consistent effects of experimental manipulations, which may be useful for quantitative characterisation of experimental and therapeutic manipulations of motor disorders.