A system for making anastomoses between hollow structures by mechanical means is provided with a device in the shape of an annular or tubular element comprising circumferentially provided means, such as pin-shaped elements, for joining the abutting walls of the hollow structures together. An applicator is intended for moving said annular or tubular element in position and activating the joining means thereof, so as to make the anastomosis. Possibly, intraluminal joining means can be inserted without using an annular or tubular element.