The　control　problems　of　a　flexible-base　and　flexible-joint　space　manipulator　with　uncertainties　were　addressed,　and　a　mixed　control　scheme　was　proposed　based　on　adaptive　robust　terminal　sliding　mode　control　and　adaptive　optimal　vibration　control.　Firstly,　the　system　was　reduced　to　a　slow　subsystem　and　a　fast　subsystem　by　singular　perturbation　method.　Secondly,　a　trajectory-tracking　adaptive　robust　terminal　sliding　mode　control　scheme,　including　an　equivalent　control,　a　robust　control,　and　an　adaptive　adjusting　algorithm,　was　presented　for　the　slow　subsystems.　And　then,　a　vibration　optimal　control　strategy　was　proposed　based　on　adaptive　state　observation　for　the　fast　subsystems.　The　simulation　results　show　the　validity　of　the　proposed　scheme　in　rigid　and　flexible　motion　controls　of　the　system.　©　2019,　China　Mechanical　Engineering　Magazine　Office.　All　right　reserved.