Summary: We propose blind source separation techniques that are applicable to a wide class of source distributions that may be skewed or symmetric and may even have zero kurtosis. Skewed distributions are encountered in many important application areas such as communications and biomedical signal processing. The methods stem from the maximum likelihood approach. Powerful parametric models based on the extended generalized lambda distribution and the Pearson system are employed in finding the score function. Model parameters are adaptively estimated using conventional moments or linear combinations of order statistics (L-moments). The developed methods are compared with the existing methods quantitatively. Simulation examples demonstrate the good performance of the proposed methods in the cases where the standard independent component analysis methods perform poorly.