This Ph.D. thesis is devoted to the development of a specific semi-analytical algorithm especially well-suited to derive the long-term evolution of near geosynchronous space debris and based on the concept of mean orbital motion. In a first approach, the semi-analytical theory is concerned with the singularity issues arising for circular and equatorial orbits as well as with the geostationary resonance modeling. In a second part, motivated by the discovery of high area-to-mass ratios space debris in high altitude Earth's orbit (mostly near the geosynchronous region), the direct radiation pressure models are revisited and completed. Within this context, the main effects of the direct solar radiation pressure for the mid- and long-term evolution of both the eccentricity and the inclination vectors are analyzed through a well-suited model. Moreover, by means of a smart extension, the passage in the Earth's shadow is taken into account in the computations of the orbits. Finally, a further insight into the intrinsic stability of such space debris is performed, by means of a recent numerical technique (MEGNO) which is based on the concept of ``variational chaos indicator'.