Abstract: This invention relates to a system for packing packaging units in packaging boxes, having for both substantially rectangular boundaries and a rectangle-shaped supporting surface, comprising the following components, a package feeding track for feeding the packaging units, a box feeding track for feeding the empty packaging boxes, a box discharge track for discharging the filled packaging boxes, a gripper head for engaging the packaging units and placing these from a pick-up portion of the package feeding track into the packaging boxes at a filling location of the box discharge track, and a control unit for executing successive packing cycles, wherein all movements of the moving components mentioned are performed in a single vertical plane, wherein the movement for placing the packaging units in the packaging boxes proceeds exclusively vertically.