In vitro models of rhythms of cognitive relevance, such as gamma (30-80 Hz) and theta (5-12 Hz) rhythms in the hippocampus, demonstrate an absolute requirement for phasic inhibitory synaptic transmission. Such rhythms can occur transiently, of approximately 1 s duration, or persistently, lasting for many hours. In the latter case, stable patterns of interneuron output, and their postsynaptic consequences for pyramidal cell membrane potential, occur despite known constraints of synaptic habituation and potentiation. This review concentrates on recent in vitro evidence revealing a division of labour among different subclasses of interneurons with respect to the frequency of persistent rhythms, and the crucial dependence on gap-junction-mediated intercellular communication for the generation and maintenance of these rhythms.