A dynamic random access memory (DRAM) device having memory cells is operated in a self-refresh mode and a normal mode. A mode detector provides a self-refresh mode signal in the self-refresh mode of operation. It includes a free-running oscillator for generating an oscillation signal independent of the self-refresh mode signal. In response to the oscillation signal, a self-request controller provides a self-refresh request signal in the self-refresh mode. The self-refresh signal is asynchoronized with the self-fresh mode signal and is provided to an address circuit to select a wordline for refreshing the memory cells thereof. The self-refresh request controller includes logic circuitry for arbitrating timing between initial active edges of the oscillation signal and the self-refresh mode signal and providing the self-refresh request and ceasing it, regardless of conflict between the self-refresh mode signal and the oscillation signal upon self-refresh mode entry and exit. The DRAM devices perform and achieve reliable self-refresh for variable DRAM cell retention time.