In an awake state, neurons in the cerebral cortex fire irregularly and EEG recordings display low-amplitude, high-frequency fluctuations. During sleep, neurons oscillate between ‘on’ periods, when they fire as in an awake brain, and ‘off’ periods, when they stop firing altogether and the EEG displays high-amplitude slow waves. However, what happens to neuronal firing after a long period of being awake is not known. Here we show that in freely behaving rats after a long period in an awake state, cortical neurons can go briefly ‘offline’ as in sleep, accompanied by slow waves in the local EEG. Neurons often go offline in one cortical area but not in another, and during these periods of ‘local sleep’, the incidence of which increases with the duration of the awake state, rats are active and display an ‘awake’ EEG. However, they are progressively impaired in a sugar pellet reaching task. Thus, although both the EEG and behaviour indicate wakefulness, local populations of neurons in the cortex may be falling asleep, with negative consequences for performance.