Abstract We describe the cellular mechanisms that underlie the generation of the K-complex, a major grapho-element of sleep electroencephalogram in humans. First we demonstrate the similarity between K-complexes recorded during natural sleep and under ketamine-xylazine anaesthesia in cats. Thereafter, we show by means of multi-site cellular and field potential recordings that K-complexes are rhythmic at frequencies of less than 1 Hz (mainly 0.5–0.9 Hz) and that they are synchronously distributed over the whole cortical surface as well as transferred to the thalamus. The surface K-complex reverses its polarity at a cortical depth of about 0.3 mm. At the cortical depth, the K-complex is made of a sharp and high-amplitude negative deflection that reflects cellular depolarization, often preceded by a smaller-amplitude, positive slow-wave reflecting cellular hyperpolarization. The sharp component of the K-complex may lead to a spindle sequence and/or to fast (mainly 20–50 Hz) oscillations. K-complexes appear spontaneously or triggered by cortical or thalamic stimulation, and they arise within cortical networks. We suggest that K-complexes, either in isolation or followed by a brief sequence of spindle waves, are the expression of the spontaneously occurring, cortically generated slow oscillation.