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Singular systems have been the subject of interest over the last two decades due to their many practical applications. But it has to be said that system identification of such system is still a challenging area because of the difficulty of identification of such systems for their complex structures. In addition, it seems that by developing a useful method for identification of singular system, one can use the useful property of such systems in describing the natural complex phenomena. This paper presents a novel methodology for identifying nonlinear singular systems from empirical data. Singular systems are idealized models for systems with slow and quick modes of change. However, their identification is a challenging problem even for the linear case. A new learning method, generalized locally linear model tree (GLoLiMoT) algorithm is introduced. The contribution of this paper is to provide a method for adjusting the parameters of fuzzy descriptor model, e.g. the splitting ratio and the standard deviation, the number of locally linear neurons or the number of linear singular systems for the consequent part in fuzzy descriptor model as well as the order of the singular system. By these modifications an accurate model of nonlinear singular system is obtained which is compared with several other methods in two case studies. Results depict the power of the proposed approach in describing nonlinear complex phenomena.