An elongate self-closing sleeve for protecting at least one elongate member, said sleeve comprising 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 configured to receive said at least one elongate member, and wherein said warp knitted textile comprises at least one first monofilament yarn that forms laying-in stitches, the at least one first monofilament comprising a plastic material.