This paper addresses the observer design problem for a class of nonlinear descriptor systems whose nonlinear terms are slope-restricted.The full-order observer is formulated as a nonlinear descriptor system.A linear matrix inequality (LMI) condition is derived to construct the full-order observer.The existence and uniqueness of the solution to the obtained observer system are guaranteed.Furthermore,under the same LMI condition and a common assumption,a reduced-order observer is designed.Finally,the design methods are reduced to a strict LMI problem and illustrated by a numerical example. This paper addresses the observer design problem for a class of nonlinear descriptor systems. These nonlinear terms are slope-restricted. The full-order observer is formulated as a nonlinear descriptor system. A linear matrix inequality (LMI) condition is derived to construct the full- order observer. The existence and uniqueness of the solution to the obtained observer system are guaranteed. Still more, under the same LMI condition and a common assumption, a reduced-order observer is designed. Finally, the design methods are reduced to a strict LMI problem and illustrated by a numerical example.