A method and the associated devices for implementing a suspend-to-RAM (STR) mode of operation in a computer system utilizing the self-refreshing capability of synchrotron DRAM. To switch into the STR mode of operation, system memory data in a first control chip (the north bridge) is first transferred to a memory unit under the direction of a second control chip (the south bridge). The voltage level at the clock-enable pin of the system memory is pulled down under the direction of the south bridge or the north bridge. Power to the north bridge is cut upon receiving a signal from a basic input/output system.