Abstract: The modes of relative motion in three moving planes associated with the orbital station are considered: rectilinear separation and approach of tethered objects; hovering of the tethered object relative to the vertical equilibrium position; circular flight of the tethered object around the orbital station; separation of the tethered object from the orbital station upon approaching a rectilinear trajectory; approach of the tethered object to the orbital station with transition to a spiral trajectory; and revolution of the tethered object around the orbital station with simultaneous approach to/removal from the station. These modes exhibit the variety of possible maneuvers implementable using tether systems. © Pleiades Publishing, Ltd. 2025.