The modern astrometric catalogues UCAC4 [1], PPMXL [2] and XPM [3] - with full coverage of the sky - contain millions of entries and provide qualitatively new material, particularly for investigating the kinematics of nearby stars in both Galactic hemispheres separately. Unfortuna tely, due to strong correlations of the parameters, the standard LS solutions of the Ogorodnikov-Milne equations on hemispheres cannot be trusted. To remedy this we use an approach, the rst step of which is the expansion of proper motions in a system of vector spherical harmonics which are orthonormal on a hemisphere. In the second step, the kinematic parameters are derived from the coecients of the expansion. This approach was rst used by Vityazev and Tsvetkov [4] for a kinematic analysis of the proper motions listed in the astrometric catalogues Hipparcos [5], Tycho-2 [6] and UCAC3 [7]. In the current paper, this technique is applied to the extensive present-day catalogues UCAC4, PPMXL and XPM containing up to 108 stars.