The main focus of this work is to efficiently determine the double-outage contingencies that threaten the operation of the power system.This work is necessary because enormous numbers of double-outage contingencies exist for even relatively small systems, and new standards require system operators to begin considering more than single-outage contingencies.Without an efficient method for predicting the severe contingencies, the entire set of double-outage contingencies has to be solved, and this means solving many millions of contingencies.Several algorithms are presented to detect double-outage contingencies that result in violations.The algorithms use varying amounts of information.However, at most they use linear sensitivities, line limit information, and line flow information.The output of the screening algorithms is compared to the full set of results for the double-outage contingency analysis, solved using the dc power flow.The results show that, even using a very limited amount of information about the system, it is possible to predict a very high percentage of the double-outage contingencies that result in violations.