The　trajectory　tracking　and　vibration　suppression　control　of　free-floating　space　flexible　manipulator　system　with　an　attitude　controlled　base　were　discussed.　After　feedback　linearization,　the　slow　and　fast　subsystems　were　obtained　by　using　singular　perturbation　theory.　Then,　a　two-time　scale　fuzzy　logic　controller　for　coordinated　motion　between　the　base＇s　attitude　and　the　manipulator＇s　joints　of　space　flexible　manipulator　system　was　designed.　The　slow-subsystem　fuzzy　logic　controller　dominated　the　trajectory　tracking　of　coordinated　motion.　The　fast-subsystem　controller　damped　out　the　vibration　of　the　flexible　link　by　optimal　linear　quadratic　regulator　(LQR)　method.　Numerical　simulation　results　illustrate　that　the　proposed　controller　is　reliable　and　effective.