In this paper, an efficient and reliable neural active power filter (APF) to estimate and compensate for harmonic distortions from an AC line is proposed. The proposed filter is completely based on Adaline neural networks which are organized in different independent blocks. We introduce a neural method based on Adalines for the online extraction of the voltage components to recover a balanced and equilibrated voltage system, and three different methods for harmonic filtering. These three methods efficiently separate the fundamental harmonic from the distortion harmonics of the measured currents. According to either the Instantaneous Power Theory or to the Fourier series analysis of the currents, each of these methods are based on a specific decomposition. The original decomposition of the currents or of the powers then allows defining the architecture and the inputs of Adaline neural networks. Different learning schemes are then used to control the inverter to inject elaborated reference currents in the power system. Results obtained by simulation and their real-time validation in experiments are presented to compare the compensation methods. By their learning capabilities, artificial neural networks are able to take into account time-varying parameters, and thus appreciably improve the performance of traditional compensating methods. The effectiveness of the algorithms is demonstrated in their application to harmonics compensation in power systems.