1. The dynamics of the centre mechanism of individual cat X retinal ganglion cells is investigated. The visual stimuli consist of temporal contrast modulation of stationary patterns. In order to study the response of the centre mechanism, patterns were either sine gratings of high spatial frequency or small circular spots positioned over the receptive-field centre. 2. Responses to contrast reversal are approximately linear. However, as the modulation depth of the stimulus increases, responses become more transient. Ganglion cell responses show this phenomenon at moderate contrasts (e.g. 0.1), which do not elicit discharges that approach the maximum firing rate of the ganglion cell. 3. A sequence of dynamical models are constructed from responses elicited by sum-of-sinusoids modulation of the spatial pattern. The first model is strictly linear. It consists of a series of low-pass filters and a single high-pass filter. The linear model predicts the approximate shape of the step response, but does not account for the change in shape of the response as a function of modulation depth. 4. The second model, a quasi-linear model, allows the 'linear' dynamics to vary slowly with a neural measure of contrast. The main effect of high contrast is a shorter time constant in the high-pass filter. This model accounts qualitatively for the increased transience of the response, but fails to predict the magnitude of the effect at higher modulation depths. 5. In the third model, the transfer characteristics of the centre response adjust rapidly as contrast changes. This intrinsically non-linear model provides excellent agreement with observed response to steps and more complex modulation patterns. 6. The non-linearity necessitated by a voltage-to-spikes transduction is analysed quantitatively. In most ganglion cells, a simple truncation at 0 impulses/s (and no saturation) explains the changes in apparent gain and mean firing rate that occur as modulation depth is increased. A non-linear voltage-to-spike transduction per se cannot account for the observed effect of contrast on dynamics. 7. The parameters of the dynamical model are measured for a population of twenty-seven X ganglion cells (nineteen on-centre and eight off-centre). The low-pass stage and the strength of the high-pass stage are relatively uniform across the population. The over-all gain and the dynamics of the high-pass stage vary substantially across the population, but show no consistent dependence on the on-off distinction or on retinal location. Some implications of this variability for retinal function are discussed.