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This paper presents an alternative approach using the differential logic associated to artificial neural networks (ANNs) in order to distinguish between inrush currents and internal faults for the protection of power transformers. The study of the current distortion originated from current transformer (CTs) saturation is one of the main aims of the work. The alternative transients program (ATP) has been chosen as the computational tool to simulate a power transformer under fault and energization situations. The radius basis function (RBF) neural network is proposed as an alternative approach in order to distinguish the situations described, using a smaller amount of data for the training purpose if compared with networks such as the multilayer perceptron (MLP). The MLP neural network with the backpropagation method is also implemented for comparison purposes. A wide range of architectures is evaluated and the work shows the best net configurations obtained. The ANN results are then compared to those obtained by the traditional differential protection algorithm. Encouraging results related to the application of the new method are presented.