A vehicle transmission system includes an input shaft connected to a differential mechanism, which has two output shafts. The two output shafts carry first and second coaxially mounted sun wheels, respectively, of an epicyclic gear system which mesh with first and second sets of planet wheels, respectively, which mesh with first and second annulus wheels, respectively. Each planet wheel is mounted to rotate independently about a respective planet shaft and the planet shafts are connected to a common carrier, which is rotatably mounted coaxially with the first and second sun wheels. The first and second annulus wheels are connected together. The carrier is connected to selectively operable speed changing device arranged to increase or decrease the speed of rotation of the carrier about its axis.