Abstract: A bolt-on part, especially a front or rear bumper, of a motor vehicle, that can be exposed especially in its outer wall to impact energy and is mounted pointwise on a structural member of a motor vehicle, with the connection between the structural member and the bolt-on part consisting of pin-shaped fastening devices on one of the two parts to be connected and recesses in the other of the two parts, is intended to dissipate as much deformation energy as possible by coming loose from the structural member under the influence of an impact in the lengthwise direction of the bolt-on part. For this purpose, at least one of the recesses in each case is closed circumferentially and is located at the end furthest away in the direction of action from the point where the impact energy is applied. The other recesses are open circumferentially and are in the form of grooves inclined at less than .alpha.=90.degree.