The　trajectory　tracking　and　vibration　suppression　control　of　free-floating　space　flexible　manipulator　with　an　attitude　controlled　base　are　discussed.　With　the　law　of　conservation　of　momentum,　the　Lagrangian　principle　is　utilized　to　model　the　dynamic　function　of　the　space　flexible　manipulator　incorporating　the　assumed　modes　method.　Using　singular　perturbation　theory,　a　slow　subsystem　describing　the　rigid　motion　and　a　fast　subsystem　corresponding　to　the　flexible　motion　are　obtained.　Then,　a　composite　controller　for　coordinated　motion　between　the　base＇s　attitude　and　the　manipulator＇s　joints　of　space　flexible　manipulator　system　is　designed.　The　slow-subsystem　partitioned　neural　network　controller　dominates　the　trajectory　tracking　of　coordinated　motion　in　joint　space　in　the　presence　of　unknown　parameters.　The　fast-subsystem　controller　damps　out　the　vibration　of　the　flexible　link　by　fuzzy　logic　controller.　Numerical　simulation　results　illustrate　the　effectiveness　of　the　proposed　controller.