The　dynamics　modeling　and　the　fast　fault-tolerant　vibration-attenuation　control　of　the　elastic-base　flexible-arm　space　robot　with　actuator　gain　fault　and　deviation　fault　are　investigated.　According　to　the　linear　spring　theory,　assumed　mode　method　and　the　second　Lagrange　equation,　the　dynamical　model　of　the　elastic-base　flexible-arm　space　robot　is　constructed.　A　finite-time　fault-tolerant　control　scheme　is　designed　for　the　system　by　combining　the　dual-power　non-singular　fast　terminal　sliding　mode　(DNFTSM)　with　the　dual-power　fast　approaching　law,　and　the　stability　of　the　closed-loop　system　is　proven　by　using　Lyapunov　function　method.　Then　the　hybrid　trajectory　is　introduced　to　renew　the　fault-tolerant　controller,　and　a　DNFTSM　finite-time　fault-tolerant　vibration-attenuation　control　method　on　the　base　of　the　virtual　control　input　is　formulated.　The　novelty　of　the　proposed　control　technique　lies　in　realizing　the　trajectory　tracking　of　the　spacecraft　attitude　and　the　manipulator　joints　and　eliminating　the　linear　deformation　of　the　elastic　base　and　the　nonlinear　vibration　of　the　flexible　arm　through　only　one　controller　in　a　short　period　of　time.　The　simulation　results　reveal　that　compared　with　the　conventional　computed-torque　vibration-attenuation　control　method,　the　error　convergence　rate　of　the　designed　method　has　increased　by　75%　and　the　amplitude　of　the　elastic　base　is　reduced　by　two　orders　of　magnitude,　which　can　be　limited　within　4.0　×　10–6 m.　Hence,　the　effectiveness　and　feasibility　of　the　presented　control　strategy　are　verified.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Austria,　part　of　Springer　Nature　2023.