Slow-wave sleep as well as generalized absence seizures are characterized by the occurrence of synchronized oscillations in thalamocortical systems that spontaneously appear and disappear. The spontaneous appearance of synchronized oscillations results from the initiation by one or a small number of cells followed by the progressive recruitment of large numbers of neighboring neurons into the synchronized network activity. Synchronized network oscillations representative of slow-wave sleep, as well as absence seizures, were demonstrated to cease spontaneously at least in part through the persistent activation of a hyperpolarization-activated cation conductance. Block of this conductance resulted in oscillations that, once generalized, occur continuously. These results indicate that the persistent activation of a hyperpolarization-activated cation conductance is a key mechanism through which synchronized oscillations in thalamocortical networks normally terminate.