This technical note considers the observers design for a class of nonlinear singular systems. The approach is based on the new parameterization of the generalized Sylvester equations solutions. The conditions for the existence of these observers are given and sufficient conditions for their stability are derived using linear matrix inequalities (LMIs) formulation. Reduced-order, minimal-order and full-order observers are designed by a unified method. A numerical example is presented to demonstrate the effectiveness of the developed method.