At present, thousands of space debris are located in Earth’s orbits. It has a different size ranging from a few millimeters to tens of meters. Tethered systems are promising technology to de-orbit the space debris. The tethers have been proposed for reduction of space debris either through momentum transfer or use of electrodynamic effects. Another possible way to remove the large space debris from the critical areas of near-Earth orbit is using a tethered space tug attached to the space debris. Large space debris can strongly affect the motion of the space tug and the tether during the transportation process, which can lead to the loss of control of the tethered system. The problem of removal a large space debris from the orbit to the Earth’s surface is studied. The space transportation system is composed of two bodies connected by the tether. The first body is a space debris (upper rocket stage or a large nonfunctional satellite) and the second body is a space tug. The spatial motion of the system is studied in the gravity field of the Earth under the action of the space tug thruster, aerodynamic drag and the gravitational torque. Osculating elements of the orbit are used to describe the motion of the center of mass of the system. Particular attention is given to investigate the spatial motion of the space debris relative to the tether and to the space tug. The influence of the initial conditions and the properties of the system on the motion of the system is studied.