Aimed　at　the　problems　of　flexible-link　flexible-joint　space　manipulator　with　parameter　uncertainties　and　external　disturbances　to　track　the　desired　motion,　the　T-S　fuzzy　control　and　double-flexible　vibration　parallel　control　were　proposed.　Firstly,　a　joint　flexibility　compensation　controller　was　introduced　to　improve　the　equivalent　stiffness　of　each　joint.　Secondly,　the　error　dynamic　equations　were　obtained　based　on　feedback　linearization　in　the　trajectory　tracking　procedure,　and　control　parameters　of　fuzzy　control　was　selected　by　Lyapunov　stability　theory.Subsequently,　the　fuzzy　sliding　mode　control　was　improved　with　simple　T-S　fuzzy　rules.　The　great　advantage　of　proposed　control　is　free　of　undesirable　chattering　phenomenon　in　sliding　mode　control　and　light　burden　of　computations.　Then,　the　double-flexible　parallel　control　was　presented　to　suppress　the　vibration　of　flexible　links.　Finally,　the　simulation　results　on　a　space　manipulator　demonstrate　the　validity　of　the　proposed　control　scheme.　©　2016,　China　Mechanical　Engineering　Magazine　Office.　All　right　reserved.