A system for supplying power to a volatile semiconductor memory having a memory array, with the semiconductor memory being provided with a standby voltage that is present at a second connection of the semiconductor memory. To implement the power supply system as simply and with as few components as possible, the semiconductor memory is provided with a stabilization circuit for stabilizing the standby voltage that has a low impedance when the input voltage is elevated and a high impedance when the input voltage is too low to supply the semiconductor memory.