This research focused on developing an on-line contingency filtering scheme for dynamic security analysis.;Severity ranking and analysis of contingencies is thought of as a filtering process. The most severe cases are identified and ranked high on the contingency list while the non-severe cases are filtered out of the list. A cascade of progressively restrictive contingency filters is used. Three levels of filters are used. Each level of filter is divided into an inertial transient and post-inertial transient period. The first two levels of filters are very fast and approximate, but most conservative. The third level of filter uses exact analysis. The inertial transient filters capture cases which are potentially severe with respect to the inertial transient period. On the other hand, the post-inertial transient filters are designed to capture cases which are potentially severe with respect to the post-inertial transient period. These filters make use of the signatures left by the power system during the inertial transient period. The tool used in the analysis is a sparsity based direct method which is based on the exit point technique.