The present disclosure concerns an elongate self-closing sleeve for protecting elongate members, said sleeve having internal and external opposite faces wherein said sleeve comprises a sound dampening textile substrate and a warp knitted textile stitched to said textile substrate. Said sound dampening textile substrate and said warp knitted textile having first and second longitudinal opposite free edges biased toward each other in order to define an internal space wherein said elongate member could be placed therein, and wherein said warp knitted textile comprises at least one first monofilament yarn that forms laying-in stitches and that is in plastic material(s).