The invention relates to an agricultural machine that is suitable for the harvesting of grain-like crops, comprising a header (1), attached to the front of the machine at adjustable height, the header comprising a first cutting device (2) whose position is determined by the adjustable height of the header, and a second cutting device (7), comprising a knife drum (7) that is rotatably mounted in a housing (6), which via rollers (8) or equivalent support means can move over the ground at different heights of the header, and wherein the housing (6) of the knife drum on the back of the header (1) is connected via at least two coupling systems (10), each of these systems comprising a lower and an upper support arm (15, 16), which are pivotally connected to the header, and with the housing of the knife drum, whereby the position of the housing (6) remains substantially unaltered by the different height settings of the header (1).