To　realize　the　rigid　motion　control　and　flexible　vibration　suppression　of　flexible-base　flexible-joint　space　robot　with　unknown　parameters,　a　dual-adaptive　control　scheme　based　on　the　non-certainty　equivalence　principle　was　proposed.Applying　the　Lagrange　method,　the　momentum　conservation　principle　and　the　singular　perturbation　method,　the　system　dynamic　equations　and　its　corresponding　slow　and　fast　subsystems　in　two-time　scale　were　derived　when　the　base　was　in　the　attitude-controlled　operation　mode.A　new　type　of　low-pass　filter　signal　was　utilized　to　modify　the　regression　matrix　of　system,　and　then　a　non-certainty　equivalence　adaptive　control　strategy　with　adjustable　multiple　parameters　was　designed　for　the　slow　subsystem　to　accomplish　trajectory　tracking　of　the　base＇s　attitude　and　joints　of　robot　with　unknown　parameters.For　the　uncertain　fast　subsystem,　an　adaptive　control　was　presented　to　ensure　the　asymptotic　stability　of　the　fast　subsystem　and　suppress　the　flexible　vibration　of　the　base　and　joints.The　simulation　results　demonstrate　the　effectiveness　of　the　dual-adaptive　scheme　in　the　rigid　and　flexible　motion　control　of　the　system.　©　2019,　Editorial　Board　of　Journal　of　Huazhong　University　of　Science　and　Technology.　All　right　reserved.