(1) Abastumani Astrophysical Observatory, Abastumani, Georgia
(2) Institute of Theoretical Astronomy, St.Peterburg, Russia
The investigation of the long-period orbital evolution of geostationary satellites (GS) under the influence of gravitational and nongravitational forces is rather complicate problem. (1) It is shown, that the selection of the proper co-ordinate system, based on Laplace plane, permits to simplify the solution of Lagrange equations due to linearization of secular perturbations and small change of orbital inclination because of luni-solar attraction. (2) Then, the solution of equation for stroboscopic longitude due to resonant perturbations from geopotential can be find with aid of hyperelliptical quasi-integrals, which are defined numerically. (3) The software of elaborated method of orbital evolution is used for calculation of ephemerides and identification of GS observations over long-term intervals. This method is used also for calculation of improved orbits for GS Catalogue, and for investigation of the structure of GS ring. (4) The rate of calculation of GS evolution for one year with PC IBM - 386 is equel to 2-4 sec.