The invention relates to a winding device and to a method for covering wall openings or windows. The winding device comprises a covering element that can be rolled up, a deflecting element that has a wave-like design, or is simply formed by a bottom hemline, or a bottom woven fabric edge and/or longitudinal edge, and at least on raising and lowering unit. In addition, the covering element is provided with an upper longitudinal edge, which is preferably arranged in parallel to the deflecting element. The lower longitudinal edge is either connected to the deflecting element, or is formed by the same, so that as a result of a rotation of the deflecting element, or of the lower woven fabric edge and/or longitudinal edge, about a horizontal axis, the covering element can be rolled up or down.; The raising and lowering unit comprises at least one cord, wherein at least one free end of the cord is connected to the raising and lowering unit. The cord is arranged such that it encloses the covering element, so that the deflecting element, or the lower longitudinal edge, is guided in the bend of the cord. The at least one cord can be guided in two opposite directions of movement that are relative to one another.