Inter- and intrahemispheric EEG relationships were studied as a function of maturation in new-born infants. The spatio-temporal organization of EEG activity obtained during the two stages of sleep described in new-born infants - quiet sleep and active sleep - was analysed in 9 full-term new-born infants and 5 prematures (6 records). EEGs were recorded through transverse parietal montage made up of six bipolar derivations. Two epochs of 1.5 min each - successively obtained in both stages of sleep - were digitized, filtered in three frequency bands (beta, theta and delta) and computer-processed according to two methods, factor analysis and rhythms averaging. 1. The following EEG characteristics were found in both groups: (a) Instability of frequency within each frequency band (beta, theta and delta). However, theta activity was the most stable of the three, especially in quiet sleep. (b) Variability of topographical organization (i.e., localization of maxima of potentials) from one moment to another in both stages of sleep and in the three frequency bands. In spite of this intra-individual variability some sort of "average structure" was found in all infants; it was characterized by usually lateral and often symmetrical positions of the maxima of potential on the two hemispheres. For the same infant this structure was the same in the three frequency bands. (c) Poor interhemispheric relationships under all conditions, as well as poor interregional links in one hemisphere. 2. Some EEG characteristics differentiated the two groups and thus seemed to be related to maturation. Compared to full-term newborns the premature group showed: better stability for all three activities, especially for beta activity; higher frequency and larger amplitude of beta activity; better inter- and intrahemispheric relationships; fewer differences related to sleep stages. These results are discussed in terms of organization of the underlying cortical generators. The authors suggest that the active areas would increase in number and in surface with maturation, whereas the links between these different separate areas would remain very poor in the human full-term new-borns as well on one hemisphere as across hemispheres. This last finding would argue against the hypothesis that the corpus callosum which, as is well known, matures early, plays an important role in the establishment of interhemispheric links.