A process for mounting an elastic hinge on eyeglass frames, for coupling a first pivot element, which comprises an elastic carriage provided with a head portion having a first hole, with a second pivot element comprising two shoulders provided with second holes. The head portion of the first pivot element comprises a tilted slide surface adjacent to the first hole. The process envisages to insert the head portion in a slit between the shoulders of the second pivot element to place in succession their holes offset from each other, and then engaging a hinge pin in the holes, so that the free end of the hinge pin acts in abutment against the slide surface of the head portion, in order to force the carriage to slide until the first hole of the first pivot element is aligned with the second holes of the second pivot element.