The　angle　tracking　and　flexible　vibration　suppression　integrated　control　for　the　two　flexible　links　free-floating　space　robot　with　joint　torque　output　dead-zone　and　external　disturbance　are　discussed.　The　hybrid　trajectory　concept　with　rigid　motion　and　flexible　mode　is　introduced,　and　an　adaptive　control　scheme　of　the　integral　sliding　mode　neural　network　based　on　the　integration　of　motion　and　vibration　is　proposed.　In　case　the　slope　and　boundary　of　dead-zone　is　uncertain　and　the　upper　kind　of　the　optimal　approximation　error　is　unknown,　the　compensation　term　of　the　scheme　can　eliminate　the　effect,　and　ensures　the　robustness　of　the　rigid　motion.　Also,　the　scheme　suppresses　the　vibration　of　the　two　links　flexible　actively　to　improve　the　tracking　performance.　Simulation　results　show　that　the　scheme　can　achieve　the　integration　control　of　the　motion　and　vibration　effectively.　©　2020,　The　Editorial　Board　of　Journal　of　System　Simulation.　All　right　reserved.