Due to the “square” law of the variation of centrifugal force with speed, a centrifugal governor is not well suited to variable-speed engines with a wide range of speeds. It lacks power at low speeds, which results in poor idling, and it has an excess of power at high speeds. Also the presence of heavy weights and springs may give rise to undesirable resonance phenomena. This paper deals with the development and gives the theory of a variable-speed hydraulic governor consisting of a positive displacement pump and of a pressure-operated plunger. Such an arrangement should be distinguished from a hydraulic relay as used in servo-governors. The story of its development is told, starting from the simplest possible scheme. The various troubles experienced are reported, together with the way in which they were overcome, leading to the design of a production type hydraulic governor meant primarily for road transport compression-ignition engines. A mathematical theory of the hydraulic governor is derived and the conditions for stable governing established, as well as the criteria for a definite convergency of the disturbances set up by a sudden change of engine load. The magnitude of the temporary increase of engine speed following a sudden throwing-off of its load is calculated. The results of the mathematical analysis are discussed and illustrated by some numerical examples. These compare quite well with the results of experiments carried out on the engine. Some of the conclusions arrived at, and the formulae derived, are applicable to variable-speed governors of any type. A hydraulic governor which was developed as a result of the research described underwent several hundreds of hours of bench testing, as well as many thousands of miles of road testing.