Synchronized multiple bursts represent an epileptic neuronal behavior transitional between synchronized single bursts (interictal spikes) and self-sustained seizures. As described in the previous paper, synchronized multiple bursts occur in hippocampal slices treated with picrotoxin. Multiple bursts consist of an initial prolonged depolarizing burst followed by a rhythmical series of afterdischarges. Both the initial burst and the afterdischarges are synaptically elicited. Our previously described model of the interictal spike illustrates that the generation of a single synchronized burst requires a neuronal network possessing the following properties: intrinsic bursting capability of individual neurons, the presence of recurrent excitatory connections between principal neurons and the blockade of synaptic inhibition. The model demonstrates that the generation of single synchronized bursts involves the initial excitation of one or more neurons, and the subsequent sequential spread of excitation through a population of neurons via recurrent excitatory synapses. In the present study, we examined whether this same mechanism assumed in the previous model could also allow for the generation of synchronized afterdischarges in a population of neurons. We tested the effects of manipulating three network factors: synaptic strength, synaptic density and the refractoriness in the population members following a period of excitation. We discovered that the refractory period following prolonged excitation assumed in our previous model was insufficient to allow for afterdischarge generation. Once sufficient refractoriness was introduced, afterdischarges appeared in our network of neurons. In the present study, the required refractoriness was attributed to the properties of pyramidal cell axons. In principle, such refractoriness might be located elsewhere in the network. The possible contribution of axonal properties is emphasized because of the known intermittent conduction in other axons. Our present model also reproduced other experimental data. Thus, if the network was too small or if synaptic strength was too small, then only a single synchronized burst occurred. The basic assumptions of this model are both biologically plausible and experimentally testable. © 1984.