A neuronal network model of epilepsy is investigated. The network is described in terms of differential delay equations in which strong depolarization of any unit in the ensemble results in spike inactivation and the attenuation of that cell's output. It can be shown that homogeneous oscillations with the qualitative features of epileptic seizures, including the progression from tonic to clonic firing patterns, appear when a highly depolarized homogeneous steady state becomes unstable. Stability calculations and the study of a simplified model that is solved analytically point to hyperexcitation as a critical determinant of epileptic activity. Spatially inhomogeneous solutions were studied in three types of connective topologies, i) uniformly densely connected networks, ii) densely connected networks containing a number of cells (microfoci) with pathologically strong connections to each other and to other normal cells, and iii) sparsely connected networks in which the strength of connections falls off as a function of the physical distance separating the cells. Homogeneous epileptic solutions remain stable to spatial perturbations in the first two types of topology. Type iii) may however give rise to a variety of spatiotemporal patterns, including travelling waves and "chaotic" behaviour. It is suggested that such inhomogeneous patterns may occur in the early stages of a seizure.