Reliable operation of electrical power systems in the presence of multiple critical N - k contingencies is an important challenge for the system operators. Identifying all the possible N - k critical contingencies to design effective mitigation strategies is computationally infeasible due to the combinatorial explosion of the search space. This paper describes two heuristic algorithms based on the iterative pruning of the candidate contingency set to effectively and efficiently identify all the critical N - k contingencies resulting in system failure. These algorithms are applied to the standard IEEE-14 bus system, IEEE-39 bus system, and IEEE-57 bus system to identify multiple critical N - k contingencies.