A machine tool system has a machine tool with a stationary machine base, support elements connected to the machine base, and a crossbeam connected to the support elements. The crossbeam is adjustable relative to the support elements in a Z-direction or the support elements are adjustable relative to the machine base in an X-direction. A tool holder head is mounted on the crossbeam and adjustable for travel in a Y-direction along the crossbeam. The X-, Y- and Z directions form a cartesian coordinate system. A control facility is connected to the machine tool for controlling travel in the Y-direction and adjustment in at least one of the X- and/or Z-directions based on a kinematic parameter specified as a function of a position of the tool holder head relative to the Y-axis and thus takes into account asymmetric load distribution caused by movement of the tool holder head.