In this paper, an outlier detection method based on radial basis functions-partial least squares (RBF-PLS) approach and the Prescott test is proposed to detect outliers in complex systems. Furthermore, a robust training algorithm, weighted error back-propagation (WBP) algorithm, is also proposed to keep the training of multi-layer forward networks (MLFN) from the disturbance of outliers, if they should be retained in the data set. The experiment results fully demonstrate their satisfactory abilities on dealing with outliers and ensuring the success of modeling a complex system without clear mechanisms. (C) 2004 Elsevier Ltd. All rights reserved.