Nosepiece for eyeglass frames which comprises: a plate intended to abut against the nose of a user; a support arm for connecting the plate to the frame of eyeglasses; a cup which is extended as a prolongation of the support arm; an appendage which is projectingly extended from the rear face of the plate and is housed within the cup with two lateral faces thereof facing two lateral walls of the cup; coupling means for retaining the appendage housed within the cup. The appendage comprises a convex portion which is susceptible of rotating with respect to the cup with the surface of the convex portion in contact and in sliding-with-friction relation with the internal surface of the cup, in order to maintain the plate in the reached angular position.