Starting from known linear models for calculating the electric energy required to elaborate a heat in an electric arc furnace, new approaches based on artificial neural networks (ANN), have been studied. The effects of strongly non-linear relations between critical furnace process parameters, and other variables, not taken into account in an equation based model, have been integrated in the ANN models. Both the off-line and on-line use of models based on time series and a new system of interconnected ANNs are described. The on-line model is designed to accurately predict the end of the heat.