Due to the permanent extension of space activities, the danger generated by the larger space debris objects is increasing. Mechanisms and procedures to remove those objects should be developed in the next future. It is to be thought that the objects in LEO would be removed by putting them into an Earth atmosphere entry orbit, while those in GEO could be placed into an orbit 300 km or more higher than the nominal geostationary orbit. This paper deals with the general problem of dynamics for a system formed of a remover vehicle and a removed object. The trajectory and the attitude motion are considered for the remover and the debris. The number of degrees-of-freedom of the system is reduced, considering the joint system. Particular cases of tethered systems can be in correlation with the TERESA (Tethered Remover Satellite) concept, which has been developed by P. Eichler and A. Bode or with TOT (Tumble Orbit Transfer), initially proposed by T. Yasaka. Lagrange's equations for holonomic systems with dependent variable are used in the case the constraint equations depend of generalised coordinates. In the case the constraints equations are dependent of generalised coordinates and generalised velocities, the Lagrange's equations for non-holonomic systems are used. A model for a remover vehicle can be proposed. The spacecraft will be provided with a remote controlled tethered subsystem to be connected with the removed object. The risk of cutting the tether by small particles is considered. The remover spacecraft will be provided with several elements of tethers. In the case the tether is cut, the joint is disconnected from the removed object, and self connects to a new unit of tethers. A remover vehicle provided with two such joint spacecraft will diminish the debris collision probability of the space mission.