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We consider the problem of performing N - k security analyses in large scale power systems. In such a context, the number of potentially dangerous N - k contingencies may become rapidly very large when k grows, and so running a security analysis for each one of them is often intractable. We assume in this paper that the number of dangerous N-k contingencies is very small with respect to the number of non-dangerous ones. Under this assumption, we suggest to use importance sampling techniques for identifying rare events in combinatorial search spaces. With such techniques, it is possible to identify dangerous contingencies by running security analyses for only a small number of events. A procedure relying on these techniques is proposed in this work for steady-state security analyses. This procedure has been evaluated on the IEEE 118 bus test system. The results show that it is indeed able to efficiently identify among a large set of contingencies some of the rare ones which are dangerous.