An output data strobe signal generating method and a memory system that includes a plurality of semiconductor memory devices, and a memory controller for controlling the semiconductor memory devices, wherein the memory controller provides a command signal and a chip selecting signal to the semiconductor memory devices. One or more of the semiconductor memory devices may detect a read command and a dummy read command in response to the command signal and the chip selecting signal and generate one or more preamble signals based on a calculated preamble cycle number.