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Water and power systems are increasingly interdependent due to the growing number of electricity-driven water facilities. The security of one system can be affected by a contingency in the other system. This paper investigates a security-constrained operation problem of the energy-water nexus (EWN), which is a computationally challenging optimization problem due to the nonlinearity, nonconvexity, and size. We propose a two-step iterative contingency filtering method based on the feasibility and rating of the contingencies to decrease the size of the problem. The optimal power and water flow are obtained in a normal situation by considering the set of contingencies that can not be controlled with corrective actions. The feasibility check of the contingencies is performed in the second step, followed by a rating of the uncontrollable contingencies. Finally, the critical contingencies are obtained and added to the first step for the next iteration. We also employ convex technologies to reduce the computation burden. The proposed method is validated via two case studies. Results indicate that this approach can efficiently attain optimal values.