A Space Free-Flying Robot (SFFR) includes an actuated base equipped with one or more manipulators to perform on-orbit missions. Distinct from fixed-based manipulators, the spacecraft (base) of a SFFR responds to dynamic reaction forces due to manipulator motions. In order to control such a system, it is essential to consider the dynamic coupling between the manipulators and the base. Explicit dynamics modeling of such systems with flexible appendages is developed in this paper. The SFFR is divided into two parts, the manipulator(s), and the main base body (spacecraft) that consists of flexible appendages. The recursive Lagrangian approach is used to describe dynamics model of the flexible base system. For modeling the multi-manipulator system, a Recursive Newton-Euler approach is followed. The obtained dynamics model can be employed either numerically or symbolically. Interacting forces and torques acting between the manipulators and the main body are also modeled that could be used for simulation studies of controller design.