A power-up circuit in a computer system drives a memory device such as a dynamic random access memory (DRAM) to an initial condition after the computer system is turned on or reset. The power-up circuit also advantageously drives the memory device into the initial condition upon detecting a transient such as a negative glitch in a supply voltage being provided to the memory device. The power-up circuit includes a voltage level detector which causes a power-up signal to be provided to the memory device upon detecting that the supply voltage is less than a threshold voltage of the memory device which is necessary for the memory device to operate in an operational state. The power-up circuit also includes a delay circuit which causes the power-up signal to be provided to the memory device upon detecting that the supply voltage is beginning to rise from a quiescent voltage and at least until an amount of time determined by an RC time constant of the memory device for the memory device to enter the initial condition has passed. In response to receiving the power-up signal, the memory device enters the initial condition.