Power systems have been operating nowadays near to the stability limits putting security under risk. This is one of the reasons why the dynamic security assessment is a fundamental tool to avoid the occurrence of blackouts in the whole world. The goal is a reliable and fast way to evaluate the dynamic behavior of a power system. This dissertation deals with the problem of dynamic security assessment of power systems. The evaluation is performed based on stability margins calculated from time domain simulation results, providing qualitative information about the first swing stability. The group of severely disturbed machines is defined and the stability margins are determined. The machine with the lowest margin determines the stability margin of the system. When the system margin approaches the zero value, the critical clearing time is obtained. These outcomes are compared with that ones determined by trial and error method using a conventional transient stability program. Having done that, a contingency ranking is defined according to the critical clearing time. The ranking minimizes the number of contingencies that have to be studied. This dissertation shows that the criterion to define the group of severely disturbed machines based on the machine accelerations at the instant immediately after the fault clearing time is more efficient than that one based on the machine accelerations at the instant immediately after the fault occurrence.