One　of　the　important　issues　in　the　study　of　hybrid　stochastic　differential　delay　equations　(SDDEs)　is　the　automatic　control,　with　consequent　emphasis　being　placed　on　the　asymptotic　analysis　of　stability　and　boundedness.　In　the　study　of　asymptotic　properties,　the　robust　stability　has　received　a　great　deal　of　attention.　The　theory　of　robust　stability　shows　how　much　perturbation　a　given　stable　hybrid　SDDE　can　tolerate　so　that　its　perturbed　system　remains　stable.　Almost　all　results　so　far　on　the　robust　stability　require　that　the　underlying　SDDEs　be　either　linear　or　nonlinear　with　linear　growth　condition.　However,　little　is　known　on　the　robust　stability　of　nonlinear　hybrid　SDDEs　without　the　linear　growth　condition,　which　is　one　of　the　key　topics　in　this　paper.　The　other　key　topic　is　the　robust　boundedness.　The　aim　here　is　to　answer　the　question:　how　much　perturbation　can　a　given　asymptotically　bounded　hybrid　SDDE　tolerate　so　that　its　perturbed　system　remains　asymptotically　bounded?