A hydraulic system for an automatic transmission operatively connected to an internal combustion engine that is operable in a start-stop mode. The hydraulic system includes a hydraulic energy source to supply the hydraulic system with hydraulic energy, the hydraulic energy source including at least one electrically driven hydraulic pump to supply the hydraulic system with hydraulic energy during a stopping phase of the internal combustion engine. To achieve a reduction in fuel consumption and CO2 emissions, provision is included to enable the electrically driven hydraulic pump to be switched on in addition to a mechanically driven hydraulic pump, as needed during an operating phase of the internal combustion engine.