During the 1920s the German engineer Karl Küpfmüller made substantial advances in the development of a theory of linear systems, notably by adopting a ‘systems approach’ to modelling electrical networks and control systems. Küpfmüller's achievements included an appreciation of the significance of the ‘time × bandwidth product’ for information transmission, and the establishment of an approximate stability criterion for a certain type of control system. This early work is outlined in the context of contemporary developments outside Germany, and a brief indication is given of the scope of Küpfmüller's later career.