Active debris removal using a space tug with a tether is one of the promising techniques to decrease the population of large non-functional satellites and orbital stages in near Earth orbits. Properties of debris should be taken into account in the development of the space tugs. In this paper we consider the motion of a debris objects with fuel residuals that can affect the safety of the debris transportation process. The equations of the attitude motion of the tug-debris system in a central gravitational field are derived. Stationary solutions of the equations are found. The system of linearized equations are introduced that can be used for short term analysis. The numerical simulation results are provided that show good accuracy of the linearized equations. Proposed equations can be used to analyze the attitude motion of the tug-debris system and to determine the conventional parameters for safe tethered transportation of space debris.