An efficient computational algorithm for motion control of multi-arm free flying robots in space is discussed. For the motion control of the space manipulator mounted on a spacecraft, the movement of spacecraft itself must be considered. The generalized. Jacobian matrix is one of the good ways to solve this problem. Though an efficient computational algorithm of the generalized Jacobian was shown, it does not have a good prospect to extend to the case of multiple arms. For dexterous manipulating tasks, cooperative manipulation by multi-arm manipulators is desirable. In this paper, we show that the generalized Jacobian for multi-arm space manipulators can be obtained efficiently by regarding the total multiple-link system as a composite system which consists of two links with one joint. The proposed algorithm is applicable to any tree-structured multiple arm manipulators with not only rotational joint but also prismatic joint except close loop structure. We also show an efficient computational algorithms of the resolved acceleration control for multi-arm space manipulators.