Space　robots　are　built　very　light　in　order　to　save　expensive　launch　energy　and　to　extend　the　orbit　life,　which　results　in　considerable　link　flexibilities.　Most　of　the　present　works　are　devoted　to　space　manipulator　with　only　one　flexible　link.　Due　to　the　interactions　of　rigid　and　flexible　motion　and　the　interactions　of　flexible　motion　of　the　flexible　links,　controlling　space　manipulator　with　multi　flexible　links　is　more　complex　and　more　challenging　than　controlling　one　with　only　one　flexible　link.　Hybrid-trajectory　based　augmented　adaptive　control　was　addressed　for　free-floating　multi-flexible-link　space　manipulator　with　unknown　physical　parameters　and　external　disturbances.　The　dynamic　model　of　a　free-floating　space　manipulator　with　multi　flexible　links　was　established　by　the　momentum　conservation,　the　assumed　mode　technique　and　the　Lagrange　equations.　Based　on　singular　perturbation　approach　and　choosing　appropriate　local　coordinate　frame,　the　interactions　of　rigid　and　flexible　motion　and　the　interactions　of　flexible　motion　of　the　flexible　links　were　decoupled,　and　a　slow　subsystem　and　a　flexible-link　fast　subsystem　were　obtained.　To　suppress　the　flexible　link　vibrations,　hybrid　trajectories　of　joints　were　generated　from　terminal　trajectories　by　using　the　virtual　force　concept.　An　augmented　adaptive　controller　to　the　slow　subsystem　was　proposed　to　track　the　hybrid　trajectories.　The　hybrid-trajectory　based　augmented　adaptive　controller　ensures　that　flexible　vibrations　of　the　multi-flexible-links　space　manipulator　are　stabilized　effectively　with　good　tracking　performance.　The　virtue　of　this　control　scheme　is　that　the　linear　position,　linear　velocity,　linear　acceleration　of　the　base　needn＇t　be　measured　directly.