The　robust　control　based　on　observers　is　proposed　for　a　free-floating　flexible　space　manipulator.　Firstly　the　interactions　of　flexible　motion　of　the　two　flexible　links　are　decoupled　by　choosing　appropriate　local　coordinate　frame;　the　dynamic　model　of　a　free-floating　two-flexible-links　space　manipulator　is　established　by　the　Lagrange　equations　and　the　momentum　conservation.　Secondly　singular　perturbation　model　of　the　space　flexible　manipulator　system　is　obtained　by　using　two-time　scale　control　theory,　in　which　the　system　is　decoupled　into　slow　(rigid)　and　fast　(flexible)　subsystems.　Then　an　observer　based　robust　composite　controller　which　consists　of　a　slow　control　component　and　a　fast　control　component　is　proposed.　A　sliding　velocity　observer　based　robust　control　algorithm　is　applied　to　control　the　slow　subsystem　to　track　the　desired　trajectory.　The　fast　controller　is　designed　with　the　estimated　velocity　by　a　linear　state　observer　to　damp　out　the　vibration　of　the　flexible　links　using　optimal　Linear　Quadratic　Regulator　(LQR)　method.　Finally　the　numerical　simulation　is　carried　out,　which　demonstrates　the　controller　proposed　is　feasible　and　effective.　©　2016　Journal　of　Mechanical　Engineering.