A head for a riveting machine for applying shear rivets, the head comprising: (a) a front part and a rear part consisting of a plate and a body respectively, said plate having an axial hole for receiving the stem of a rivet and said body having an axial hole which is formed along an axis substantially coincident with axis "S" of hole formed in plate, said front part and said rear part being slidable relative to each other along a direction parallel to said axis "S"; (b) a sliding engagement assembly (39,41) arranged within a sliding chamber, defined inside said body, so as to engage a stem of a shear rivet, said engagement assembly (39,41) being capable of taking a first, advanced position and a second, retracted position inside said chamber, and in turn comprising: (b.1) a chuck having a set of radial segments or jaws arranged to engage threaded or grooved end of stem of a rivet, said chuck being slidable within sliding chamber so as to take an advanced position, in which chuck is in contact with abutment formed in correspondence with the front portion of chamber, and a retracted position, in which chuck is spaced apart from said abutment, the advanced position being taken by chuck when head is in idle condition and the retracted position being taken instead by chuck after stem of rivet has become engaged in chuck; (b.2) a flexible sleeve which has secured thereto said segments or jaws of chuck; (b.3) a ring nut held to said sleeve by means of an annular projection; (b.4) a pin for controlling the backward movement of said engagement assembly (39, 41) inside said chamber by thrusting said plate during its return movement towards said body, said pin being fastened to a radial support provided on said ring nut and being slidable within a side channel, said side channel being parallel to sliding chamber and having such an extension that it opens at the surface of body towards plate so as to let said pin come out from body; characterized in that: - a bush is fitted onto said flexible sleeve; - said ring nut surrounds said flexible sleeve; - said annular projection is an internal annular projection of said ring nut enabling said ring nut to be held between said sleeve and said bush. (a) a front part and a rear part consisting of a plate and a body respectively, said plate having an axial hole for receiving the stem of a rivet and said body having an axial hole which is formed along an axis substantially coincident with axis "S" of hole formed in plate, said front part and said rear part being slidable relative to each other along a direction parallel to said axis "S"; (b) a sliding engagement assembly (39,41) arranged within a sliding chamber, defined inside said body, so as to engage a stem of a shear rivet, said engagement assembly (39,41) being capable of taking a first, advanced position and a second, retracted position inside said chamber, and in turn comprising: (b.1) a chuck having a set of radial segments or jaws arranged to engage threaded or grooved end of stem of a rivet, said chuck being slidable within sliding chamber so as to take an advanced position, in which chuck is in contact with abutment formed in correspondence with the front portion of chamber, and a retracted position, in which chuck is spaced apart from said abutment, the advanced position being taken by chuck when head is in idle condition and the retracted position being taken instead by chuck after stem of rivet has become engaged in chuck; (b.2) a flexible sleeve which has secured thereto said segments or jaws of chuck; (b.3) a ring nut held to said sleeve by means of an annular projection; (b.4) a pin for controlling the backward movement of said engagement assembly (39, 41) inside said chamber by thrusting said plate during its return movement towards said body, said pin being fastened to a radial support provided on said ring nut and being slidable within a side channel, said side channel being parallel to sliding chamber and having such an extension that it opens at the surface of body towards plate so as to let said pin come out from body; (b.1) a chuck having a set of radial segments or jaws arranged to engage threaded or grooved end of stem of a rivet, said chuck being slidable within sliding chamber so as to take an advanced position, in which chuck is in contact with abutment formed in correspondence with the front portion of chamber, and a retracted position, in which chuck is spaced apart from said abutment, the advanced position being taken by chuck when head is in idle condition and the retracted position being taken instead by chuck after stem of rivet has become engaged in chuck; (b.2) a flexible sleeve which has secured thereto said segments or jaws of chuck; (b.3) a ring nut held to said sleeve by means of an annular projection; (b.4) a pin for controlling the backward movement of said engagement assembly (39, 41) inside said chamber by thrusting said plate during its return movement towards said body, said pin being fastened to a radial support provided on said ring nut and being slidable within a side channel, said side channel being parallel to sliding chamber and having such an extension that it opens at the surface of body towards plate so as to let said pin come out from body; - a bush is fitted onto said flexible sleeve; - said ring nut surrounds said flexible sleeve; - said annular projection is an internal annular projection of said ring nut enabling said ring nut to be held between said sleeve and said bush.