In this paper, we present an observer-based fault estimation scheme for a class of nonlinear systems where the fault enters the state and output equations via state dependent nonlinear functions. The system is reformulated as an augmented nonlinear descriptor system where the state vector comprises the system states, faults and outputs. An observer is then designed for the augmented descriptor system and it is shown that the observer states converge to the true augmented states, from which the fault is estimated. The effectiveness of the scheme is demonstrated using a nonlinear mass-spring-damper system.