A two-component zoom system creates the necessary range of magnifications, fields of view, and focal lengths of any optical zoom system. Over the last few years the utilization of the zoom systems has significantly increased, but in developing these new optical designs, designers often unnecessarily complicate an existing solution rather than develop a new design form based on theory. The developing of opto-mechanical engineering demands the design of new types of modern zoom systems: systems with a long back focal length and telecentric chief rays in image space (e.g., Canon, Angenieux, Bosch). A grapho-analytical method for the first-order design of two-component zoom systems is developed. The canonic equation ofthe components' motion is presented. It is shown that law of motion is described by third-order hyperbolae of different types. The first-order correlations between system length, components' optical powers, and possible magnification range are given. The first-order data tables for the different two-component zoom systems are presented.