This　article　focuses　on　stabilizing　highly　nonlinear　hybrid　stochastic　complex　dynamical　networks　with　time　delays　(HSCNT)　via　sampled-data　control　with　asynchronously　periodic　self-triggered　intermittent　decentralized　strategy　(SCAPI).　Considering　the　constraints　imposed　by　linear　growth　conditions　in　real　models,　we　introduce　high　nonlinearity　into　the　networks.　Moreover,　considering　the　possibility　of　nonsimultaneous　transmission　of　control　information　by　the　controllers,　the　asynchronous　decentralization　is　thus　brought　in　periodic　self-triggered　intermittent　control　for　the　first　instance.　Then,　to　resolve　the　problems　caused　by　asynchronous　decentralization,　a　graph-theoretic　approach　is　employed.　Combining　this　with　an　auxiliary　timer,　an　innovative　Lyapunov　functional　is　designed,　after　which　an　original　Lyapunov-based　method　is　proposed　to　cope　with　the　complexity　of　introducing　high　nonlinearity　and　asynchronous　decentralization　into　networks.　In　particular,　some　numerical　simulations　are　provided　for　demonstration.　©　2013　IEEE.