Displaced orbits around the collinear libration points in cis-lunar space offer significant advantages for observation and communication missions. This chapter analyzes the motion of a hybrid sail, which integrates a solar electric propulsion system with a solar sail, within the Earth-Moon Elliptic Restricted Three Body Problem. The conditions for hybrid sail displaced orbits are derived analytically, under the assumption that both the Earth-Moon system and the Sun-Earth/Moon system exhibit small orbital eccentricities. Due to the inherent instability of the quasi-periodic displaced orbits, a backstepping controller is designed to ensure long-term orbit maintenance while minimizing fuel consumption of the solar electric thruster. Illustrative examples demonstrate the effectiveness of the proposed approach.