A transmission system includes an input (22), an output (34) and an epicyclic geartrain comprising first and second gearsets. The first gearset comprises a first sun gear (2) in mesh with a set of first planet gears (4), which are rotatably carried by a first planet carrier (6) and are in mesh with a first annulus gear (8). The second gearset comprises a second sun gear (10), which is connected to rotate with the first sun gear (2) and is in mesh with a set of second planet gears (12), which are rotatably carried by a second planet carrier (14) and are in mesh with a second annulus gear (18). One of the planet carriers (6) of one of the gearsets is connected to rotate with the annulus gear (18) of the other gearset. The two connected sun gears (2), (10) and the input (22) are connected to the rotors (24, 20) of respective electric motor generators (E2, E1), the electrical stator connections of which are connected together via a controller (30) arranged to control the flow of electrical power between them. The input (22) is selectably connectable to the other (14) of the planet carriers and to the other (8) of the annulus gears by first (C2) and second (C1) selectably operable clutches, respectively, whereby the transmission system has two regimes.