In this work, we present results about the stability of near geosynchronous space debris characterized by high area-to-mass ratios. We extend previous studies by considering the influence of the Earth's shadow on the short-and long-term time evolutions. To assess the orbits stability, we use the Global Symplectic Integrator (GSI)  which consists in the symplectic integration of both Hamiltonian equations of motion and variational equations. The solution of the variational equations is then used to compute the Mean Exponential Growth factor of Nearby Orbits (MEGNO) chaos indicator. The effects of the Earth's shadow are analyzed using the adapted conical and cylindrical Earth's shadowing models introduced by . Our stability study shows that the Earth's shadow greatly affects the global behaviour of space debris orbits by increasing the size of chaotic regions around the geostationary altitude.