A two-block technique is proposed for on-line transforms the trajectories of a multi-machine system contingency screening, ranking and assessment in transient stability studies. Its design relies on a hybrid direct - time-domain method called SIME. Basically, SIME assesses stability by transforming the multi-machine power system parameters into those of a one-machine infinite bus system, then by calling upon the equal-area criterion. Stability margins thus obtained are used to classify contingencies, select the "interesting" ones and, finally, rank and assess these latter. An 88-machine EPRI test system illustrates the technique and shows its ability to correctly handle the simulated contingencies, while complying with real-time computational requirements.