Abstract <p>A method of forming a space tether system in low-Earth orbit in the form of a pyramid is considered, at the base of which there is a square with terminal satellites rotating relative to the central spacecraft. The process of building a pyramidal configuration of a tether system includes the following steps: 1) formation of a rotating system in the form of a square; 2) separation of the satellite on a tether from the central spacecraft in the direction perpendicular to the plane of the square and its transfer to a given state, characterized by the finite length of the tether and the relative speed. As a result, the tether system is a geometric pyramidal structure that maintains an unchanged orientation in a fixed geocentric coordinate system, which is assumed to be inertial. It is shown that the structural stability of such a system сan be provided using a low-thrust engine located on a satellite located at the top of the pyramid. The two characteristic positions of the pyramid are compared in relation to the orbital plane of the center of mass of the system (the axis of the pyramid is perpendicular to the plane of the orbit and belongs to it) and the best position is selected in terms of the minimum required thrust to stabilize the motion of the system. A fairly simple model of satellite motion (located at the top of the pyramid), constructed using Lagrange equations, is used to conduct a comparative analysis of alternative options, analyze system dynamics, and synthesize control algorithms. To verify the feasibility of the proposed approach, a more complete model of the system’s motion in a geocentric fixed coordinate system is used, taking into account the extensibility of tethers, the one-sidedness of mechanical connections, the operation of tether release mechanisms, and errors in separating the satellite from the central spacecraft.</p>