The long-term stable vascular prosthesis (1) is a plaited textile structure, the multiple filaments (2) of which consist of a thermoplastic material having a melting range and being highly elastically textured; at least individual filaments (3) at least at a certain number of crossing points (4) of the filaments (2) are bonded firmly to one another, for example adhesively bonded. This produces a vascular prosthesis (1) having a radial expansion of the order of magnitude of that of a natural vein; at the same time, the prosthesis has a required minimum seam tear-out strength. <IMAGE>