Some forms of electrographic seizures are generated at the level of the cortical network. Neocortical kindling exhibits a resistance to produce generalized convulsive seizures, and therefore, it was rather difficult to use it to study the cortical epileptogenesis. Here, using supra-threshold cortical kindling, we report electrophysiological patterns of field-potential synchronization and intracellular activities in chronically implanted non-anesthetized cats, during different states of vigilance, and during acute seizures elicited by prolonged (20–60 s) electrical stimulation. Acute seizures were easily elicited during transition from slow-wave sleep (SWS) to waking state. The seizures were mainly clonic accompanied with tonic components followed by prolonged postictal depression. Delayed rhythmic outlasting activities (OA) at ˜ 1.5 Hz, first time reported here, followed the postictal depression, and lasted up to 2 h. These activities were clear during waking state, slightly reduced during SWS and completely absent during rapid-eye movement sleep. They started focally and following daily stimulations generalized over the entire cortical surface. Extra- and intracellular neuronal recordings during OA displayed spike-doublets, built on the summation of successive excitatory postsynaptic potentials and fast-prepotentials, entailing an increased dendritic excitation. Our results suggest that such rhythmic long-lasting oscillatory activity outlasting seizures are the key factor of epileptogenesis, leading to epilepsy.