There is evidence that sleep is important for memory consolidation, but the underlying neuronal changes are not well understood. We studied the effect of sleep modulation on memory and on neuronal activity in a memory system of the domestic chick brain after the learning process of imprinting. Neurons in this system become, through imprinting, selectively responsive to a training (imprinting) stimulus and so possess the properties of a memory trace. The proportion of neurons responsive to the training stimulus reaches a maximum the day after training. We demonstrate that sleep is necessary for this maximum to be achieved, that sleep stabilizes the initially unstable, selective responses of neurons to the imprinting stimulus, and that for sleep to be effective, it must occur during a particular period of time after training. During this period, there is a time-dependent increase in EEG activity in the 5-6 Hz band, that is, in the lower range of the theta bandwidth. The effects of sleep disturbance on consolidation cannot be attributed to fatigue or to stress. We establish that long-term trace consolidation requires sleep within a restricted period shortly after learning. Undisturbed sleep is necessary for the stabilization of long-term memory, measured at the behavioral and neuronal levels, and of long-term but not short-term neuronal responsiveness to the training stimulus.