A speed monitoring circuit is disclosed for an automatic positioning system. This speed monitoring circuit composes a measurement of the actually present speed determined from measurement signals generated by an incremental position measuring device with the desired speed commanded by the positioning system. The difference between the actual and commanded speed is detected and, in the event of an excessive deviation, a warning or an automatic termination of operation of the positioning system is provided. In the disclosed system, the desired speed is determined by a controller in which a digital computer calculates the difference between the instantaneous position of one relatively movable machine component and the desired position of the movable component as established by programmed data.