Abstract: Apparatus operable to fasten together overlying metal sheets has a cooperating piercing-and-forming punch and die set, which partially sever and displace a localized region of the sheets out of the planes thereof, and a flattening punch which then operates to spread the displaced region sideways and fasten the sheets together with a clenching action. A die mounting for said piercing-and-forming die and a punch mounting for said flattening punch are sequentially and separately operable, respectively, by two hydraulical piston and cylinder arrangements which effect movement thereof relatively to said piercing-and-forming punch. An associated control system comprises pressure sensing devices which sense the operating pressures in hydraulic feeds respectively supplying the piston hydraulic cylinders.