Motor-vehicle bumper assembly

A bumper arrangement (1) for a motor vehicle, in particular for a lower load plane, wherein the bumper arrangement (1) has a bumper crossmember (2) and two spaced-apart supporting profiles (3, 3), the first ends (4, 4) of which are each fastened indirectly or directly to one of the two regions of the bumper crossmember (2) that are in the vicinity of the end and which are each fastened at a second end (5, 5) to chassis parts or longitudinal member parts (6) formed on the motor vehicle, wherein the bumper crossmember (2) is held by the supporting profiles (3, 3) on the vehicle structure and has a preferably symmetrically curved portion (7) in the form of a portion of a tube or a portion of a groove or a portion of a profile, wherein the portion (7) is fastened by its ends (8, 8′) in the vicinity of the second ends (5, 5′) of the supporting profiles (3, 3′) to the chassis parts or longitudinal member parts (6), wherein the curved portion (7) is shaped in a manner projecting with a central region (9) to the bumper crossmember (2) and therefore at least lies against the bumper crossmember (2).