The problem of the control of the object cooperative manipulation during the work of multiple non-redundant six degrees-of-freedom manipulators is considered in this paper. The problem of the cooperative manipulation control is, like all its problems, solvable only if the system is considered as the elastic one, taking into account all existing constraints. The controlled system is with the output number greater than the available number of inputs, therefore, in the first stage the desired motions are selected from the set of the possible nominal ones, containing the trajectories of the manipulated object mass centre and slave manipulators contacts. Afterward, the classification of control tasks is performed. The procedure for the calculation of the driving torques introduced into the joints of the manipulators, necessary to obtain the nominal trajectory tracking, is proposed. The theoretical analysis of cooperative system closed loop behaviour is exposed, particular attention being paid to the uncontrolled variables. The procedure is illustrated on the example of the simple closed loop cooperative system, consisting of the manipulated object and two one degree-of-freedom manipulators. For this system, the behaviour is determined and the driving torques are calculated.