In 25 healthy subjects at resting with their eyes closed and open, a current phase structure of the EEG was measured, i.e. a trajectory and velocity of oscillation spreading over the head surface in temporal-occipital area. Visual computer multiplication revealed stable individual specifics of the EEG "running wave" dynamics which were then confirmed independently proceeding from the statistical significance criteria. Some subjects had characteristic transversal modulations of the EEG waves (from the left fo the right and vice versa), other subjects manifested longitudinal modulations along the diagonal from the cortex left anterior areas to the right posterior those (in some of them) or along the same diagonal in the opposite direction (in others). When opening the eyes, the character of the EEG "running wave" undergoes dramatic changes. Among other parameters, a growth of the trajectory share occurs in occipital area along with acceleration of the "running wave" spreading on all other trajectories. Both effects are bound to each other and the sharper dynamics is specific for subjects characterised as sympathotonic those as compared with para-sympathotonic.