This paper presents the relations between the slow (< 1 Hz) oscillation (characterizing the activity of corticothalamic networks during quiescent sleep in cats and humans), sleep K-complexes, and some paroxysmal developments of sleep patterns. At the cellular level, the slow oscillation is built up by rhythmic membrane depolarizations and hyperpolarizations of cortical neurons. The EEG expression of this activity is marked by periodic K-complexes which reflect neuronal excitation. The slow oscillation triggers, groups and synchronizes other sleep rhythms, such as thalamically generated spindles as well as thalamically and cortically generated delta oscillations. We discuss the distinctness of the slow (< 1 Hz) and delta (1-4 Hz) oscillations. We also show that the slow cortical oscillation underlies the onset of spike-wave seizures during sleep by transforming the periodic K-complexes into recurrent paroxysmal spike-wave complexes.