This article presents normal EEG characteristics and their maturational pattern in premature infants of 24-30 weeks gestational age. Although the very premature infants with a normal outcome are not that numerous, their normal EEG pattern should be known, as EEG constitutes a basis for neurological prognosis. Background activity is first discontinuous but the discontinuity gradually decreases and the activity is completely continuous at 30 weeks of age, during active sleep. At the same time, interburst intervals become shorter so that the proportion of time without EEG activity decreases. Based on EEG activity and eyes movements, a rough sleep state differentiation appears as early as 25 weeks of gestational age and is complete at 30 weeks. The main EEG figures are high-voltage delta waves, whose frequency is slower and amplitude higher in younger infants. Temporal delta waves occur in sequences and are characteristic of the very premature infant; they progressively become smaller and less numerous and disappear around 27-28 weeks. In contrast, occipital delta waves remain numerous; they are of high voltage and usually bilaterally superimposed with fast rhythms. Both types of frontal delta waves that are seen in 24-27 weeks premature babies disappear with maturation. Bursts of synchronized delta waves, which are less numerous than localized delta waves, also disappear before 28 weeks of gestational age. Finally, diffuse theta bursts which are mainly recorded at 26-27 weeks, progressively focus on temporal areas with maturation. At 30 weeks, they are observed on temporal areas, mainly during slow-wave sleep.