This paper presents dynamical modeling of topologically stacked structure of general underactuated mechanisms. Underactuation may arise when a manipulator includes at least one passive joint which is either a free joint where torque propagating along the axis of rotation is only due to friction, or a flexible joint which has passive elements introducing stiffness and damping. In this regard, free flying platform can be considered as linked to a fixed base by six DOF free joints with no friction. Dynamics of underactuated cooperating manipulators become a bigger challenge when underactuation is encountered by the combination of free, flexible and active joints based on a free-flying platform in no-gravity setting. We call this class of systems as "general underactuated systems". This paper demonstrates the use of an order of N algorithm for the dynamical modeling of general underactuated manipulators cooperating to perform a common task on a free-flying space platform.