The invention relates to a hydraulic system for an automatic gearbox, more particularly a dual-clutch gearbox, for a motor vehicle, comprising a high-pressure circuit (H) which includes a pressure accumulator (25), at least one clutch (K1, K2) and actuators (22), and comprising a low-pressure circuit (N) for cooling the clutch (K1, K2), the high-pressure circuit (H) and the low-pressure circuit (N) each containing a hydraulic cooling pump (59) and a hydraulic charging pump (53) that can be driven by a shared electric motor (57); and comprising a controller (39) which, when it is detected that the pressure accumulator needs to be charged, controls the electric motor (57) to run at a charging setpoint speed (n
soll, laden ), and/or, when it is detected that cooling is needed or another need exists, controls the electric motor (57) to run at a cooling setpoint speed or another setpoint speed (n
soll, kühlen ). According to the invention, when the pressure accumulator does not need to be charged and there is no need for cooling and no other need, the controller (39) reduces the setpoint speed (n
soll ) to zero for a specified period (Δt
aus ). At the end of the period (Δt
aus ) the controller (39) controls the electric motor (57) to run at least at the test speed (n
prüf ).