A longitudinal study of EEG and neuropsychological memory parameters of 20 children with signs of intellectual endowments combined with social communication difficulties have been carried out. The data of gifted children is compared to data of students in regular school. The neurophysiological study was conducted with the participation of children of 7–16 years old, and children of 7–12 years participated in in the study of memory parameters. Gifted children of 7–12 years compared to age norm have demonstrated better memory value and more stable EEG-pattern with law theta, alpha-3, and beta-3 activities, and increased activity of alpha-1 and beta-2 frequency ranges. We chose to study the integral index of "alpha + beta / delta + theta" that reflects the main manifestation of the "growing" brain bioelectrical activity in school-age children. Normally, this indicator gradually increased from primary school age to youthful, while gifted children was significantly lower than normal, and only after 14 years it increases abruptly and reaches normative values to 16 years. It has been suggested that delay in the formation of high-frequency components of EEG alpha-rhythm is representative of the maturation of neural networks in this group of intellectually gifted children and adolescents.