Recent results support the view that inspiration gets inhibited and terminated when a centrally generated inspiratory activity (CIA) combined with afferent activity from pulmonary stretch receptors has grown to a critical threshold. CO2 acts both to increase the rate of rise of CIA and to raise the 'off-switch' threshold. Body temperature affects only the growth rate of CIA but not the threshold. Once switched off, inspiration is kept inhibited for the subsequent expiration with a decaying power that can be strongly modulated by different reflexes. The rostral pontine "pneumotaxic" structures provide the 'off-switch' mechanism with a threshold lowering input but do not seem to form part of the oscillating network. Thus, it appears that the basic network for respiratory rhythmicity depends on excitation and inhibition between the two basic neural mechanisms: the CIA-generator, and the 'off-switch mechanism. The necessary non-linearities are provided for by the threshold function of the 'off-switch' and the decay of the inhibition, which keep inspiration turned off during expiration.