Abstract: An infinitely variable gear transmission system for vehicles includes a differential gear unit for input, an epicyclic gear unit, two hydraulic pumps and a hydraulic circuit having direction control valves and orifices, intercoupling the two hydraulic pumps, one of the hydraulic pumps rotating with the first output shaft of the differential gear unit and one of the three gear elements of the epicyclic gear unit, and the second hydraulic pump rotating with the second output shaft and the second gear element, and a control unit to selectively control the direction and the fluid pressure in the hydraulic circuit and control the speed of the third gear element in clockwise and anticlockwise direction. In another embodiment the hydraulic circuit includes a flow control valve with variable orifice and a controller to continuously check and control the opening of the orifice, and correct the fluid pressure for the exact output speed.