A sheet-fed stamping press (10*) comprising a foil application unit (2*) designed to allow transfer or lamination of foil material onto successive sheets (S), which foil material is fed to the foil application unit (2*) in the form of a foil carrier (FC) 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 (S) 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 (S) and the foil carrier (FC) against an outer surface of the stamping segments (211*; 211**), the foil carrier (FC) being supplied by the foil feeding system between the sheets (S) and the stamping segments (211*; 211**), and wherein each counter-pressure unit is designed as a cylinder unit 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 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 (FC) 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 (S) 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 (S) and the foil carrier (FC) against an outer surface of the stamping segments (211*; 211**), the foil carrier (FC) being supplied by the foil feeding system between the sheets (S) and the stamping segments (211*; 211**), <EOS>