The invention contemplates an improved mechanical traction drive with a hydraulically implemented single control whereby a desired range of speed ratios between input and output shafts is selectively available, without requiring clutch connection to the power source, such as a battery-operated electric motor. The transmission employs a combination of completely mechanical friction-roller and meshing-gear planetary systems which are connected at all times, whether the single control is operated to call for a forward drive or a stop, and whether the motor is run in the direction to produce a forward or a reverse drive of the output shaft. Provision is made for automatically downshifting and upshifting the transmission via hydraulic means, in response to input-torque requirements and/or output-torque limitations.