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The neural network (NN) approach to power system transient stability analysis (TSA) has been presented as a potential tool for online applications, but the high dimensionality of the power systems turns it necessary to implement feature extraction techniques to make the application feasible in practice. At the same time, feature extraction can offer sensitivity information to help the identification of input features best suited for control action. This paper presents a new learning-based nonlinear classifier, the support vector machines (SVMs) NNs, showing its suitability for power system TSA. It can be seen as a different approach to cope with the problem of high dimensionality due to its fast training capability, which can be combined with existing feature extraction techniques. SVMs' theoretical motivation is conceptually explained and they are applied to the IEEE 50 generator system TSA problem. Aspects of model adequacy, training time and classification accuracy are discussed and compared to stability classifications obtained by multi-layer perceptrons (MLPs). Both models are trained with complete and reduced Input features sets.