<div>In order to answer the most pressing scientific questions about the two Martian moons, Phobos and Deimos, new remote sensing observations are required. The best way to obtain global high resolution observations of Phobos and Deimos is through dedicated missions to each body that utilize close-proximity orbits, however much of the orbital tradespace is too unstable to realistically or safely operate a mission.</div><div><br></div><div>This thesis explores the dynamics and stability characteristics of trajectories near Deimos. The family of distant retrograde orbits that are inclined out of the Deimos equatorial plane, known as quasi-satellite orbits, are explored extensively. To inform future mission design and CONOPS, the sensitivities and stability of distant retrograde and quasi-satellite orbits are examined in the vicinity of Deimos, and strategies for transferring between DROs are demonstrated. Finally, a method for designing quasi-satellite science orbits is demonstrated for a set of notional instruments and science requirements for a Deimos remote sensing mission.<br></div>