Hydro-Quebec has a long interest in on-line Dynamic Security Assessment (DSA) driven by its challenging system dynamics. Presently, off-line calculated security limits are combined with an on-line monitoring system. However, new developments in dynamic simulation enable real-time or near-real-time DSA calculations and transfer limits determination. In this paper, the domain-decomposition-based algorithm implemented in the simulator RAMSES is presented, along with techniques to accelerate its sequential and parallel executions. RAMSES exploits the localized response to disturbances and the time-scale decomposition of dynamic phenomena to provide sequential acceleration when the simulation is performed on a single processing unit. Additionally, when more units are available, the parallelization potential of domain-decomposition methods is exploited for further acceleration. The algorithm and techniques have been tested on a realistic model of the Hydro-QuÃ©bec system to evaluate the accuracy of dynamic responses and the sequential and parallel performances. Finally, the real-time capabilities have been assessed using a shared-memory parallel processing platform.