We use vector spherical harmonics for a kinematic analysis of the proper motions of stars from the Hipparcos, Tycho-2, and UCAC3 catalogues in the northern and southern Galactic hemispheres. We have found that the statistically reliable values of the Ogorodnikov–Milne model parametersM+ 32 andM − 32 have different signs in different hemispheres. This is a consequence of the Galaxy’s rotational retardation with distance from the principal Galactic plane. Based on various samples of stars from the above catalogues, we have obtained the following estimate for the magnitude of the vertical gradient of Galactic rotation velocity in the solar neighborhoods: (20.1 ± 2.9) <|∂V/∂z| <(49.2 ± 0.8) km s−1 kpc−1. Another result that is revealed by our analysis of the parameters M − 13 and M+ 13 in different Galactic hemispheres is that the vertical gradient of expansion velocity for the stellar system ∂VR/∂z is positive in the northern hemisphere and negative in the southern one. This suggests that the expansion velocit