A self-refresh control device may be provided. The self-refresh control device may include a refresh signal output circuit configured to generate self-refresh signals with an oscillator and provide a refresh signal. The self-refresh control device may begin a self-refresh mode in response to a clock enable signal and a self-refresh signal within a self-refresh entry period, and may prevent performance of a new self-refresh operation by delaying an additional self-refresh signal until after the self-refresh entry period has ended.