Abstract: The invention concerns a connecting device for anastomosis of a vascular prosthesis to a tubular conduit in which a lateral or terminal opening has been formed, the prosthesis including, at a connecting end, a turned-back portion forming an annular layer whose free edge is adapted to be pressed onto the immediate vicinity of the rim of the tubular conduit. The connecting device includes a set of fasteners each of which is adapted to press the annular layer onto the rim of the opening. It further includes an annular support along which the fasteners are distributed. The fitting device includes a connecting device and a releasable holding mechanism for holding the fasteners in the open position. The implant comprises a vascular prosthesis and a fitting device.