The S-tree method is used to investigate the problem of the mutual motion of the substructures of the Local Group galaxies, as well as of the velocity of the Local Group itself. The different degree of mutual influence between the Local Group galaxies is estimated which will affect the star forming and other individual properties of the galaxies. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via 3D reconstruction procedure, which uses the information on the radial velocities of the galaxies, but not on their distances. The Local Group velocity in the CMB frame is also estimated: VLG -> CMB = 668 km/s pointing toward galactic coordinates l=265 and b=42.