The main objective of this work has been the connection between the Ogorodnikov-Milne model (OM) and the Spherical Harmonic development (SH) for different kinematic observables. This new approach allow us to benefit from the high orthogonality, easy extension to high orders and no appearance of the distance in the SH expansions; and also to benefit from the intrinsic meaning of the OM parameters. This work (a complete description will appear in Hernández-Pajares & Núñez, 1991, Astron. J., submitted) completes the theoretical studies started in Hernández-Pajares & Núñez (1990a, Astrophys. Space Science 170, 187 and 1990b, Error, bias and uncertainties in Astronomy, ed. Jaschek and Murtagh, Cambridge Univ. Press, 339).