Space debris is internationally recognised as hazard to current and future space activities. This proposal will investigate the orbital dynamics of space debris through semi-analytical models of their motion under the effect of orbit perturbations. The long-term evolution will be investigated through formulations obtained by averaging techniques of the dynamics equations. This will allow a deeper insight into orbit debris evolution under the effect of natural orbit perturbations in the Earth environment. It will be possible to identify resonance conditions for quasi-equilibrium orbits for space debris objects. In the current state of the art particular focus is given to Geostationary Earth Orbits and Low Earth Orbits region, as space activities are mostly concentrated in these areas. In this research we aim at building a general catalogue of families of frozen orbits for debris fragment. The definition of these orbits will potentially suggest novel ways of active debris removal by identifying natural sinks orbit where debris can be naturally collected. Moreover, techniques previously developed for the deflection of Near Earth Objects will be extended to design optimal trajectories for interception and deflection or active removal of space debris. A formulation of the debris problem will be developed, which allows assessing the effectiveness of any proposed mitigation strategy. Methodologies for the design of optimal transfers to the interception of space debris will be studied. Once first guess solutions for the overall mission have been identified, a selected number of refined trajectories can be optimised, using a more accurate model of the system dynamics. In this context, this research aims to study and develop techniques for the solution of the optimal control problem associated to the design of low-thrust trajectories, in order to fully exploit the problem dynamics within the optimisation process, and to provide robustness in convergence.