A DLL of a memory device having a normal mode and a power down mode includes a clock buffer for buffering an external clock signal to output an internal clock signal. A power down mode controller generates a power down mode control signal to define the normal mode or the power down mode in response to a clock enable signal. A source clock generation unit receives the internal clock signal to generate a DLL source clock signal under the control of the power down mode control signal. A phase update unit performs a phase update operation based on the DLL source clock signal to output a DLL clock signal.