On-orbit servicing, active debris removal or assembling large structures on orbit are only some of the tasks that could be accomplished by space robots. In all these cases, a contact between a space robot and the satellite being serviced, deorbited, or assembled will occur. This contact results in a contact force exerted on the space robot, and therefore momenta of the space robot system are no longer conserved. Most of the papers that are concerned with motion planning problems of a space robot manipulator either consider that no external forces or moments are acting on the space robot system or use additional controllers when the space robot is subjected to external forces and moments. Such a controller minimizes end-effector position and orientation errors caused by the changes in system momenta due to external forces and moments acting on this system. The novelty of this work is that it proposes a new method for planning the motion of dual-arm space robot manipulators when linear and angular momenta of the space robot system are not conserved due to external forces and moments acting on the space robot base or/and manipulators' end-effectors. In the proposed method the changes in system momenta are considered, but no additional controllers are needed. In this paper, we derive the motion planning equations for dual-arm space robot manipulators, where external forces and moments are acting on both satellite and manipulator end-effectors. The proposed method has been verified by numerical simulations, and the results are presented and discussed.