The　control　problem　of　coordinated　motion　of　a　free-floating　flexible　space　manipulator　system　is　discussed.　Based　on　the　assumed　mode　method,　the　system　linear　momentum　conversation　and　the　Lagrange　equation　of　second　kind,　the　second-order　nonlinear　dynamic　equation　of　the　flexible　space　manipulator　system　is　established.　Accordingly,　using　the　Backstepping　control　approach,　the　Backstepping　control　scheme　is　designed　for　coordinated　motion　between　the　base＇s　attitude　and　the　joints　of　the　free-floating　flexible　space　manipulator　system.　With　the　proposed　control　scheme,　the　system　satisfies　the　condition　of　Lyapunov　stability　theory,　and　it　has　global　asymptotic　stability.　A　planar　free-floating　flexible　space　manipulator　system　is　simulated　to　verify　the　effectiveness　of　the　proposed　control　scheme.