A change in the human psychophysiological state, caused by stress in particular, affects the processes of autonomic control, the activity of which is reflected in infra-slow oscillations of brain potentials with a frequency of less than 0.5 Hz. We studied the infra-slow oscillations in scalp electroencephalogram (EEG) signals in the frequency ranges of 0.05–0.15 Hz and 0.15–0.50 Hz that are associated with the processes of sympathetic and parasympathetic control, respectively, in healthy subjects at rest and during stress-inducing cognitive tasks. The power spectra of EEG signals, the phase coherence coefficients, and indices of directional coupling between the infra-slow oscillations in the signals of different EEG leads were analyzed. We revealed that, compared with the state of rest, the stress state is characterized by a significant decrease in the power of infra-slow oscillations and changes in the structure of couplings between infra-slow oscillations in EEG leads. In particular, under stressful conditions, a decrease in both intrahemispheric and interhemispheric coupling between EEG leads occurred in the range of 0.05–0.15 Hz, while a decrease in intrahemispheric and an increase in interhemispheric couplings was observed in the range of 0.15–0.50 Hz.