Interictal spikes are a simple kind of epileptic neuronal activity. Field potentials and intracellular recordings observed during interictal spikes of penicillin-treated slices of the hippocampus were reproduced by a mathematical model of a network of 100 hippocampal neurons from the region including CA2 and CA3. The model shows that this form of neuronal synchronization arises because of mutual excitation between neurons, each of which is capable of intrinsic bursting in response to a brief input.