The　velocity　observer　based　adaptive　control　of　flexible-joint　free-floating　space　manipulators　with　parametric　uncertainties　and　modeling　errors　is　addressed.　First,　the　dynamical　model　of　a　free-floating　space　manipulator　with　two　flexible　revolute　joints　is　established　by　the　Lagrange　equations.　Second,　a　flexibility　compensator　was　proposed,　which　could　make　the　equivalent　joint　stiffness　large　enough　to　use　traditional　singular　perturbation　approach.　Based　on　singular　perturbation　theory,　the　system　is　decomposed　into　two　subsystems,　a　slow　subsystem　and　a　flexible-joint　fast　subsystem.　Then　a　composite　controller　which　consisted　of　a　slow　control　component　and　a　flexible-joint　fast　control　component　was　proposed.　A　sliding　velocity　observer　based　augmented　adaptive　control　algorithm　was　applied　to　control　the　slow　subsystem.　The　flexible-joint　fast　controller　was　designed　with　the　estimated　velocity　by　linear　observer　to　stabilize　the　fast　subsystem　around　the　equilibrium　trajectory　set　up　by　the　slow　subsystem　under　the　effect　of　the　slow　controller.　Finally,　numerical　simulations　were　carried　out,　which　showed　that　elastic　joint　vibrations　had　been　stabilized　effectively　with　good　tracking　performance.　©　2014　IAA.　Published　by　Elsevier　Ltd.　All　rights　reserved.