Dynamic　modelling　and　robust　control　of　a　free-flying　flexible-link　flexible-joint　space　manipulator　with　an　elastic　base　are　investigated.　In　this　system　there　are　unknown　but　bounded　external　disturbances　and　parameters.　First　the　dynamic　model　of　a　free-flying　space　manipulator　with　two　flexible　links,　two　flexible　joints　and　an　elastic　base　is　established　by　the　momentum　conservation　and　the　Lagrange　equations.　Second　based　on　singular　perturbation　approach　and　choosing　appropriate　local　coordinate　frame,　the　interactions　of　rigid　and　flexible　motion　and　the　interactions　of　flexible　motion　are　decoupled,　and　a　singularly　perturbed　model　has　been　derived.　This　singularly　perturbed　model　consists　of　a　flexible-joint　fast　subsystem,　a　flexible-link　elastic-base　fast　subsystem　and　a　rigid　subsystem.　Then　a　reduced-order　controller　is　proposed.　This　controller　consists　of　a　rigid　control　component　and　two　fast　control　components.　Based　on　the　bound　of　the　uncertainty,　a　robust　control　algorithm　is　proposed　for　the　rigid　counterpart.　A　PD　flexible-joint　fast　subsystem　controller　stabilizes　the　elastic　vibrations　at　the　joints,　and　a　optimal　flexible-link　elastic-base　fast　subsystem　controller　damps　out　the　vibrations　of　the　flexible　link　and　the　elastic　base.　Numerical　simulations　show　that　the　base＇s,　the　links＇　and　joints＇　vibrations　have　been　stabilized　effectively　with　good　tracking　performance.　Copyright　©　2018　by　the　International　AstronauticalFederation　(IAF).　All　rights　reserved.