For　the　general　requirement　of　space　robot　to　have　advantages　such　as　long　arms　and　huge　load　for　space　on-orbit　operation,　the　flexible　problem　of　mechanical　arm　should　be　considered　for　analyzing　space　robot＇s　dynamics　and　control.　The　coordinated　motion　control　and　vibration　suppression　problems　of　flexible　arm　space　robot　with　unknown　parameters　were　discussed.　With　the　law　of　momentum　conservation　and　assumed　mode　method,　the　Lagrange　principle　was　utilized　to　model　the　dynamic　function　of　flexible　arm　space　robot.　On　these　bases,　mathematical　models　which　were　suit　for　control　system　design　were　established　by　using　double　time　scale　decomposition　of　singular　perturbation　theory.　Aiming　at　the　slow-subsystem,　Radial　Basis　Function　(RBF)　neural　network　control　algorithm　with　uncertain　parameters　was　designed　to　dominate　the　trajectory　tracking　of　coordinated　motion.　The　research　purpose　of　neural　network　control　algorithm　was　to　improve　the　control　accuracy　of　whole　system　based　on　good　on-line　self-learning　of　neural　network.　For　fast-subsystem,　hierarchical　fuzzy　control　algorithm　was　used　to　control　the　vibration　of　flexible　link.　The　research　purpose　of　hierarchical　fuzzy　control　algorithm　was　to　reduce　the　size　of　fuzzy　rule　base,　and　raises　the　calculation　efficiency　of　fuzzy　controller　effectively.　Computer　simulation　results　illustrated　the　effectiveness　and　feasibility　of　proposed　algorithms.