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Catastrophe precursors are essential prerequisites for response-based remedial action schemes, at both the protective and the operator levels. In this paper, wide-area-severity indices (WASI) derived from PMU measurements serve as the basis for building fast catastrophe predictors using random-forest (RF) learning. Given the randomness in the ensemble of decision trees (DTs) stacked in the RF model, it can provide at the recall stage not only an early assessment of the stable/unstable status of an ongoing contingency but also a probability outcome which quantifies the confidence level of the decision. This methodology, which to the best of our knowledge is new to the dynamic security assessment (DSA) of power systems, is also very effective in evaluating the importance of and interaction among the various WASI input features. Our research unexpectedly showed that the ensemble of trees in the RF is very robust in the presence of small changes in the training data and generalize across widely different network dynamics. Thus, the same RF performed very well on a large database with more than 60 000 instances from a test system (10%) and an actual (90%) system combined. One such a general RF (with 210 trees) boosted the reliability of a 9-cycle catastrophe predictor to 99.9%, compared to only 70% when a single conventionally trained DT is used.