An infinitely variable transmission system for differentially steered vehicles comprises two planetary gearboxes, each coupled to drive, as output, a driving component, such as track or wheel, on either side of a vehicle. The planetary gearboxes are drivingly coupled to a power source, such as an engine or motor, via fixed gear ratio driver and via belt drive system of two or more variable ratio belt drive pulleys. Each of the two outputs of the transmission can independently and simultaneously be controlled to revolve in forward, neutral (stop), and reverse directions in a manner of continuously and infinitesimally variable speed and torque.