The　trajectory　tracking　of　elastic　base　and　double　flexible　arms　for　a　free-floating　space　robot　system　with　fully　flexible　arms　and　elastic　base　is　discussed.　The　elastic　connection　between　the　base　and　the　arm　is　considered　as　a　linear　spring　and　dynamics　model　of　the　system　which　is　regarded　as　a　two-　time　scale　system　is　derived.　For　the　slow-varying　subsystem,　the　recursive　CMAC　neural　network　(CMACNN)　which　has　good　dynamic　characteristics　is　used　to　approximate　uncertainties　of　dynamical　equation　and　a　recursive　CMAC　neural　network　control　scheme　which　improves　the　tracking　performance　is　designed　to　improve　the　tracking　trajectory　of　rigid　motion.　For　the　fast-varying　subsystem,　an　optimal　linear　quadratic　regulator　controller　is　adopted　to　damp　out　the　vibration　of　the　two　flexible　links　and　base　elastic.　Simulation　results　verify　the　effectiveness　of　the　compound　control　method.　©　2019,　The　Editorial　Board　of　Journal　of　System　Simulation.　All　right　reserved.