A DLL circuit and a synchronous memory device perform stable operation in a power down mode although the entry and exit into/from the power down mode is repeated rapidly. The synchronous memory device operates in a normal mode and a power down mode. A delay locked loop (DLL) generates a DLL clock having frozen locking information when exiting the power down mode. A controller precludes phase update operation of the DLL when a predetermined time passes after entering the power down mode to thereby obtain a time margin for a phase update operation undertaken in the normal mode.