The invention relates to eyeglasses of the rimless type comprising a bridge interconnecting the two eyeglass lenses, and two side branches of wire structure connected to respective side zones of the corresponding lenses, each side branch having a main portion together with a distal end extending said main portion and arranged to fasten to the side zone of the lens, said distal end being generally J-shaped. In accordance with the invention, each side branch is fitted with a hinge that is arranged so that the section and the profile of the side branch in its deployed position are generally continuous, thereby enabling it to pass through a through hole in the lens so as to enable said side branch to be put into place merely by being threaded, while in its deployed position, through the lens from its front face.