Singular　perturbation　adaptive　control　is　designed　for　free-flying　space　manipulators　with　multiple　flexible　links　and　unknown　physical　parameters.　The　dynamical　Lagrange　equation　was　established　based　on　assumed　mode　technique　and　linear　momentum　conservation　theory.　A　singular　perturbation　model　has　been　formulated　and　used　for　designing　a　reduced-order　controller.　This　controller　consisted　of　a　slow　control　component　and　a　fast　control　component.　An　adaptive　control　law　was　constructed　for　the　slow　counterpart　of　the　flexible　manipulator.　The　flexible-link　fast　subsystem　controller　would　damp　out　the　vibrations　of　flexible　links　by　optimal　linear　quadratic　regulator　method.　Numerical　simulations　by　undertaking　a　computer　simulation　of　a　two-flexible-link　space　manipulator　using　the　fourth-order　Runge-Kutta　integration　method　showed　that　the　link　vibrations　had　been　stabilized　effectively　with　good　tracking　performance.　©　IMechE　2014.