A sheet-fed stamping press (10*) comprising a foil application unit (2*) designed to allow transfer or lamination of foil material onto successive sheets, which foil material is fed to the foil application unit (2*) in the form of a foil carrier supplied by means of a foil feeding system, the foil application unit (2*) comprising: - a stamping cylinder with at least one circumferential stamping section provided on a circumference of the stamping cylinder and comprising successive stamping segments (211*; 211**) distributed one after the other about the circumference of the stamping cylinder, the stamping cylinder also acting as sheet-transporting cylinder and comprising multiple sheet holding units distributed about the circumference of the stamping cylinder and designed to hold successive sheets against the circumference of the stamping cylinder; and - a plurality of counter-pressure units distributed about a portion of the circumference of the stamping cylinder and designed to press the successive sheets and the foil carrier against an outer surface of the stamping segments (211*; 211**), the foil carrier being supplied by the foil feeding system between the sheets and the stamping segments (211*; 211**), and wherein each counter-pressure unit is designed as a cylinder unit (250, 255) provided with at least one circumferential pressing element positioned to cooperate with the circumferential stamping section of the stamping cylinder, characterized in that a ratio (D 21 /D 25) of a nominal diameter (D 21) of each circumferential stamping section of the stamping cylinder over a nominal diameter (D 25) of each circumferential pressing element of the counter-pressure units is an integer multiple, and in that the stamping cylinder comprises a plurality of said circumferential stamping sections provided on the circumference of the stamping cylinder, which circumferential stamping sections are distributed axially along an axis of rotation of the stamping cylinder at a plurality of axial positions, and in that each counter-pressure unit is provided with a plurality of said circumferential pressing elements that are distributed axially along an axis of rotation of the cylinder unit (250, 255) at a plurality of axial positions corresponding to the axial positions of the circumferential stamping sections of the stamping cylinder, and in that the foil feeding system is adapted to feed the foil carrier at a plurality of axial positions corresponding to the axial positions of the circumferential stamping sections, and in that a distance of each counter-pressure unit with respect to the circumference of the stamping cylinder is adjustable. - a stamping cylinder with at least one circumferential stamping section provided on a circumference of the stamping cylinder and comprising successive stamping segments (211*; 211**) distributed one after the other about the circumference of the stamping cylinder, the stamping cylinder also acting as sheet-transporting cylinder and comprising multiple sheet holding units distributed about the circumference of the stamping cylinder and designed to hold successive sheets against the circumference of the stamping cylinder; and - a plurality of counter-pressure units distributed about a portion of the circumference of the stamping cylinder and designed to press the successive sheets and the foil carrier against an outer surface of the stamping segments (211*; 211**), the foil carrier being supplied by the foil feeding system between the sheets and the stamping segments (211*; 211**),