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Correlations between individual differences in EEG characteristics of attention control systems and temperamental traits of children at the age of 11 months were studied. A sample of 88 healthy mono- and dizygotic twins at the ages of 10 to 11.5 months was examined. The EEG was recorded in the state of sustained attention to visual stimulus. Temperamental features were estimated by the Balleyguier's Questionnaire. Dependence of the scores on each of the basic temperamental traits (excitability, activity, and sociability) on the amplitudes of spectral frequency bands in 12 EEG leads was determined. To this end, the standard and stepwise linear regression techniques and multivariate discriminant analysis with training and test samples were applied. The intrapair correlations in mono- and dizygotic twins were compared in order to analyze the nature of individual differences in spectral characteristics of the EEG α range. The main results are as follows. In 11-year-old children in the state of attention, the interindividual variability of spectral amplitudes in the α band of the EEG recorded from the main cortical areas is caused, predominantly, by genetic factors. The extent of excitability inversely depends on the level of synchronization in the basic α range (6.8–7.6 Hz), which includes both the α rhythm in the retrosplenial cortical leads and the μ rhythms in the anterocentral cortical areas during sustained attention. The degree of passiveness is directly correlated with the level of synchronization in the higher subrange (8.4–8.8 Hz) of the μ rhythm in the anterocentral cortical areas during visual attention. It is suggested that certain individual differences in the temperament of one-year-old children are genetically determined by specific features of the inhibitory control over the functional state of the brain cortex.