The invention relates to a hydraulic system for an automatic transmission, in particular a dual-clutch transmission, of a motor vehicle, comprising the hydraulic cylinder (22, 23) of at least one clutch (K1, K2) and of gear selectors (G1 to G4), which hydraulic system has a pressure accumulator (25) for providing an accumulator pressure (pS) in the hydraulic system, wherein, in at least one clutchpath (30, 31) leading from the pressure accumulator (25) to the clutch hydraulic cylinder (23), a clutch valve (35), which can be controlled by an electronic control unit (39) and by means of which ahydraulic pressure present at the clutch hydraulic cylinder (23) can be set, and a pressure sensor (34), by means of which the hydraulic pressure present at the clutch hydraulic cylinder (23) can besensed, are arranged, and comprising a charging hydraulic pump (53), which, in a charging operation, pumps hydraulic fluid into the hydraulic system in order to increase the actual accumulator pressure (pS). According to the invention, the control unit (39) has a diagnostic module (79), by means of which a preload pressure diagnosis can be performed, in which the diagnostic module (79) checks charging behavior of the pressure accumulator (25) by using the pressure sensor (34) arranged in the clutch path (30, 31).