The　flexibility　of　the　joints　and　links　of　space　robots　is　considerable,　arising　from　elasticity　of　the　joints　and　links.　Controlling　such　a　robot　is　more　complex　than　controlling　rigid　one　due　to　the　interactions　of　rigid　and　flexible　motion.　Only　a　single　actuation　signal　could　be　applied　at　each　joint,　whilst　it　has　to　control　the　motion　of　the　link　joint,　the　flexure　of　both　the　joints　itself,　and　the　attached　link　for　a　flexible　space　robot.　To　investigate　such　an　underactuated　flexible-link　flexible-joint　space　robot,　a　free-floating　space　manipulator　with　one　flexible　link　and　two　flexible　revolute　joints　was　presented　in　this　paper.　The　dynamical　Lagrange　equation　was　established,　and　a　singularly　perturbed　model　has　been　formulated.　The　model　consisted　of　a　rigid　subsystem,　a　flexible-link　fast　subsystem,　and　a　flexible-joint　fast　subsystem.　Based　on　the　two-time-scale　separation　of　the　manipulator　dynamics,　a　reduced-order　controller　was　designed.　This　controller　consisted　of　a　rigid　control　component　and　two　fast　control　components.　Based　only　on　the　possible　bound　of　the　uncertainty,　an　augmented　robust　control　law　was　constructed　for　the　rigid　counterpart　of　the　flexible-link　flexible-joint　robot.　The　flexible-joint　fast　subsystem　controller　would　stabilize　the　elastic　vibrations　at　the　joints,　and　the　flexible-link　fast　subsystem　controller　would　damp　out　the　vibration　of　the　flexible　link.　Numerical　simulations　showed　that　the　link　and　joint　vibrations　had　been　stabilized　effectively　with　good　tracking　performance.　©　IMechE　2014.