This paper considers observer design for nonlinear descriptor systems. We propose approaches based on Takagi-Sugeno (TS) models. An extended estimation vector is used in order to keep the descriptor structure of the observer. The design conditions are expressed as linear matrix inequalities. The proposed observer structure, via an intermediate variable as estimated variable, is able to recover the previous observer results for TS descriptors. Moreover, through a direct extension via so-called Finsler's Lemma, relaxed conditions are obtained. Numerical examples show the effectiveness of the proposed approaches. (C) 2015 Published by Elsevier Ltd.