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The paper addresses the conventional approaches to the short-term forecasting of nonstationary processes in complex power systems using the methodology of artificial neural networks (ANNs). In many practical cases the application of different ANNs can provide a satisfactory forecast. But data preprocessing and analysis can significantly improve the forecast. In this paper the Hilbert-Huang Transform (HHT) is used as one of the most promising tools in this area. Here we focus on HHT since this transform underlies the proposed two-stage intelligent approach to short-term forecasting of nonstationary processes.