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Contingency analysis is a very demanding task in online operation of electric power systems. Amongst the many approaches proposed in literature, the application of artificial neural networks (ANN) showed promising performances, but it often failed to cope with the huge size and the large number of operative states of the real power systems. This paper presents a fast online method based on an original progressive learning ANN. Firstly, the influence zone of each outage is located. Then, a dedicated ANN is trained to forecast the post-fault values of critical line flows and bus voltages. A progressive learning variant of the radial basis function network allows fast and adaptive learning of the pre/post-fault relationships. Tests carried out on a realistic simulator based on the IEEE 118-bus system proved the feasibility of the proposed method.