A mathematical model of the space robot free-flying in the inertial space in the mode of manipulative operation was developed. It comprises explicitly the coordinates of deviation of the manipulator end point from the target. A procedure to allow for use of the manipulator self-stopping drives in the motion model was proposed. Consideration was given to some issues of permissible simplification of the space robot model. The results of numerical modeling corroborating the expected closeness of the process dynamics in the original and reduced systems under the required condition for smallness of the speed of manipulator joints were given.