An agricultural mowing machine, in particular for mowing grass, comprises a frame having a coupling device for coupling the machine to a tractor. A carrying arm is pivotally connected to the frame. A first hydraulic cylinder is configured to pivot the carrying arm relative to the frame. A lateral displacement structure is connected to the carrying arm in such a manner that the lateral displacement structure can be displaced relative to the carrying arm in a lateral direction between an inner position and an outer position. A second hydraulic cylinder is configured to move the lateral displacement structure relative to the carrying arm. A mowing unit is connected to the lateral displacement structure. The mowing unit can be moved between an approximately horizontal working position, a raised headland position, and a transport position. The first hydraulic cylinder and the second hydraulic cylinder are connected to each other in such a manner that when the mowing unit is in its transport position and the first or second hydraulic cylinder is actuated by means of pressurized hydraulic fluid, hydraulic fluid discharged from said first or second hydraulic cylinder is supplied under pressure to the other of the first or second hydraulic cylinder for pivoting the carrying arm so as to move the mowing unit from the transport position towards the headland position displacing the lateral displacement structure outwards relative to the carrying arm simultaneously.