The visual information that first-order cortical cells receive is contained in the visually evoked spike trains of geniculate relay cells. To address functional issues such as the ON/OFF structure of visual cortical receptive fields with modelling studies, a geniculate cell model is needed where the spatial and temporal characteristics of the visual response are described quantitatively. We propose a model simulating the spike trains produced by cat geniculate nonlagged X-cells, based on a review of the electrophysiological literature. The level of description chosen is phenomenological, fitting the dynamics and amplitude of phasic and tonic responses, center/surround antagonism, surround excitatory responses, and the statistical properties of both spontaneous and visually evoked spike trains. The model, which has been constrained so as to reproduce the responses to centered light spots of expanding size and optimal light and dark annuli, predicts responses to thin and large bars flashed in various positions of the receptive field. The switching gamma renewal process method has been introduced for modelling spontaneous and visually evoked spike trains within the same mathematical framework. The statistical structure of the spike process is assumed to be more regular during phasic than tonic visual responses. On the whole, this model generates more realistic geniculate input to cortex than the currently used retinal models.