One of the most complex problems in the design of practically any mechanism or machine is to select the gear ratio of an electric drive, on the basis of scientific, engineering, and economic principles. There is an extensive literature on this subject, dating mainly to the period from the 1940s to the 1960s. In current economic conditions, however, this problem is important, first, in connection with the need to find hidden reserves in existing technological equipment and, second, on account of the computerization of design systems (the availability of CAD systems) and the wide introduction of high-speed microprocessor control systems, which considerably increase production efficiency. In my view, information technologies and microprocessor control systems for electric drives, with elements of artificial intelligence and self-diagnostics, may soon permit the replacement (at least partial) of large, metalheavy, labor-intensive mechanical transmissions and gear systems. For example, the creation of microprocessor-based speed-adjustment systems and power (torque) converters seems possible even today. In addition, in real-time microprocessor control, the speed and dynamic parameters of the drive may be varied within certain limits, so as to operate as closely as possible to the optimal gear ratio or transfer function (the gear ratio as a function of the angle of rotation for lever systems). As a result, hidden reserves of the equipment may be implemented, with a perceptible economic benefit. In most research devoted to selecting the optimal gear ratio of a drive, the optimum is assumed to correspond to maximum speed of the executive mechanism or to minimum heat losses in the armature circuit of the independent-excitation dc motor, when the necessary displacement and processing time are specified. In the present work, we consider the search for the optimal gear ratio using Pontryagin’s maximum principle (from the mathematical theory of optimal processes) for both of these criteria and also for the case of minimum heat losses in the motor’s armature circuit [1]. The results obtained may be regarded to some extent as a generalization of existing research on optimal gear ratios.