The invention relates to a generally tubular prosthesis (1) for controlling the direction of flow in a duct (O) of a living organism. Said prosthesis consists of a biocompatible, elastically deformable material and comprises an annular proximal fixing part (1a) in a section (H) of the duct (O) with a greater diameter; and a distal part (1b) whose wall is designed in such a way that it can collapse on itself in the event that an overpressure is exerted on its outer surface. The diameter of said annular proximal fixing part (1a) is substantially equal to that of said section (H) of the duct (O) with a greater diameter and its resistance to crushing is significantly greater than that of the distal part (1b) of the prosthesis (1), so that the annular proximal part (1a) can retain the prosthesis (1) in the duct (O) of the living organism.