The modular transmission uses only a pair of small and light hydraulic machines of remarkably improved volumetric efficiency with pistons having body portions substantially as long as the axial length of the respective cylinders in which they reciprocate. The two hydraulic machines operate in a closed loop, one being used as a pump driven by the vehicle's engine, and the other used as a motor. Each machine has a fully articulatable swash plate. By computer control, the angles of the swash plates of the two machines are infinitely varied to provide an appropriate optimum ratio of engine/wheel speed for all conditions from start-up, city driving, hill climbing varied according to load and steepness, and over-drive for highway. This complete vehicle operation is attained while the vehicle's engine continues to operate at relatively constant speeds and relatively low RPM.