The invention concerns a multistage press, at which within the machine-mounted clamping plate (1), an insert (3) is arranged which can alternatingly be moved in the direction towards the press plunger (2) and away from it. The insert (3) is moved up and down by a cam drive actuated by the press main drive with lifting and lowering cams (5), whose cam tracks (8a, 8b) are traced by lifting rollers (6) and lowering rollers (7) under compressive prestress.Such a multistage press can be operated with a high number of strokes per minute and has, at the same time, an excellent precision of the stroke movement.