A method for the attachment of individual components (40, 42) to one another using a punch rivet, wherein at least one of the components is formed by a workpiece of composite material, wherein the punch rivet has a flange of larger diameter, a rivet section of smaller diameter and a ring-like component contact surface at the side of the flange adjacent to the rivet section and surrounding the rivet section, wherein the rivet section is formed at its free end face for the piercing of the components (40, 42), with the punch rivet furthermore having a central passage which extends over the full length of the punch rivet and the method includes the following steps: a) arrangement of a die button against one of the two components (40, 42) to be secured to one another, which are placed on one another, wherein the die button has a bore which is dimensioned to receive the rivet section, b) carrying out a relative movement of the punch rivet with the free end of the rivet section to the fore towards the components (40, 42) arranged on one another and in the direction of the die button, c) piercing of the components (40, 42) with the free end of the rivet section and introduction of the rivet section into the bore of the die button until the component contact surface comes into contact with the component adjacent to the flange, characterized by d) using a plunger in order to dilate the punch rivet at least locally, wherein the punch rivet is dilated by an axial movement of the plunger through the passage coming from the flange side of the punch rivet, with the plunger being provided with a ring shoulder which brings about the dilation, which tapers, in the direction of the free end of the plunger adjacent to the punch rivet and has a maximum diameter which is larger than the smallest diameter of the passage, and e) forming a rivet bead (80; 120) by reshaping the free end region of the rivet section in order to clamp the components (40, 42) between the flange and the rivet bead (80; 120). a) arrangement of a die button against one of the two components (40, 42) to be secured to one another, which are placed on one another, wherein the die button has a bore which is dimensioned to receive the rivet section, b) carrying out a relative movement of the punch rivet with the free end of the rivet section to the fore towards the components (40, 42) arranged on one another and in the direction of the die button, c) piercing of the components (40, 42) with the free end of the rivet section and introduction of the rivet section into the bore of the die button until the component contact surface comes into contact with the component adjacent to the flange, d) using a plunger in order to dilate the punch rivet at least locally, wherein the punch rivet is dilated by an axial movement of the plunger through the passage coming from the flange side of the punch rivet, with the plunger being provided with a ring shoulder which brings about the dilation, which tapers, in the direction of the free end of the plunger adjacent to the punch rivet and has a maximum diameter which is larger than the smallest diameter of the passage, and e) forming a rivet bead (80; 120) by reshaping the free end region of the rivet section in order to clamp the components (40, 42) between the flange and the rivet bead (80; 120).