A dynamic RAM is divided into an input circuit block responsive to an input signal supplied from an external terminal, inclusive of an operation start signal, an internal circuit block activated in response to the signal inputted from the input circuit block, and an output circuit block for outputting a signal outputted from the internal circuit block to an external terminal. A plurality of switch MOSFETs are provided in parallel between a power line for applying an operating voltage supplied from an external terminal and an internal power line for a first circuit portion in the internal circuit block, which does not need a storage operation upon reaching its non-operating state. Further, the switch MOSFETs are stepwise turned on in response to controls signals produced by delaying a start signal supplied through the input circuit block in turn, so as to perform the supply of each operating voltage.