The rhythmicity of inferior olivary neurones evoked by natural ipsilateral forepaw inputs was evaluated in the climbing fibre afferent discharge of Purkinje cells recorded in the cerebellar cortex of the decerebrate, unanaesthetized cat. Almost 50% of all Purkinje cells responding to the forepaw stimulus with an increase in complex spike activity exhibited periodic discharge, with the dominant periodicity being between 100 and 160 ms. In ten of twenty‐five neighbouring, simultaneously recorded Purkinje cells the forepaw stimulus evoked similar periodicity in their complex spike discharge. For some cells two peaks of complex spike activity were evoked by a forepaw stimulus without an obvious third peak. By altering the stimulus duration the second peak of the response was shown to be temporally uncoupled to the 'off' phase of the displacement for many cells. The interdependence of the trials contributing to the periodic peaks in the peristimulus time histogram (p.s.t.h.) was examined by a 'separation technique'. This analysis indicated that the complex spikes contributing to a specific peak in the p.s.t.h. were generated with a high degree of independence (i.e. in different trials) from the complex spikes contributing to any other peak. It was hypothesized that the independence of the rhythmic complex spike peaks is due to the long relative refractoriness following a complex spike in a single cell. Therefore, the probability of a complex spike occurring at the next one or two cycles is decreased significantly. As a consequence, an inferior olivary neurone fires usually at only one of the various peaks in response to a single presentation of the forepaw stimulus. This hypothesis predicts that stimuli evoking a complex spike at the initial peak in a high percentage of trials should give rise to less periodicity. This prediction was tested by comparing the presence or absence of evoked oscillation with the probability of evoking a complex spike in the first peak of the p.s.t.h. Cells exhibiting a probability for complex spike discharge of over 50% in the first peak showed much less periodicity than cells with a complex spike occurring in less than 50% of the trials in the first peak. These results are discussed in the context of the inferior olive being viewed as a population of coupled elements with a tendency to oscillate. The natural forepaw stimulus is hypothesized as synchronizing the phases of spontaneously oscillating climbing fibre afferents, resulting in the observed periodicity in the complex spike p.s.t.h.