A transmission device (1) with a hydraulic system (4) comprising a main transmission pump device for supplying various transmission components with hydraulic fluid. The main transmission pump device is driven by torque applied to the transmission input shaft (2). A force flow between the transmission input shaft (2) and transmission output shaft (3) is produced by various hydraulically actuated transmission components. When the hydraulic system (4) is not supplied by the main transmission pump, the force flow is interrupted. The hydraulic system (4) has an auxiliary pump device (5) by virtue of which the hydraulic system (4) too can be supplied with hydraulic fluid. The auxiliary pump device (5) is driven by torque applied to the transmission output shaft (3) at least when the force flow is interrupted.