The　partitioned　adaptive　control　and　vibration　suppression　of　free-floating　space　robot　with　flexible　arms　in　post-impact　process　are　studied.　At　first,　the　dynamic　model　of　combination　system　after　flexible　space　robot　system　capturing　a　target　system　is　established　based　on　the　collision　theory;　the　impact　effect　of　space　robot　combination　system　after　capture　operation　is　analyzed　at　the　same　time.　Secondly,　based　on　the　double　time　scale　decomposition　theory,　the　unstable　combination　system　is　decomposed　into　fast　system　and　slow　system,　representing　the　rigid　motion　of　the　system　and　the　flexible　vibration　respectively.　To　satisfy　the　compute　capacity　of　space-borne　computer　and　modular　design　concept,　the　slow　system　is　considered　as　a　set　of　interconnected　subsystems　and　a　decentralized　adaptive　neural　network　control　scheme　is　designed.　Neural　network　is　applied　to　approximating　the　unknown　dynamic　of　the　subsystems;　an　adaptive　sliding　mode　controller　is　designed　to　eliminate　both　interconnection　term　and　approximation　error.　The　control　algorithm　has　a　cutting　edge　in　independent　control　signal　and　reduced　calculation　amount.　The　Linear　Quadratic　Optimal　control　scheme　is　designed　for　fast　system　to　suppress　the　elastic　vibration　of　the　flexible　manipulators.　At　last,　numerical　example　demonstrates　the　validity　of　the　proposed　composite　control　scheme.　Copyright　©　2018　ASME.