The stability of a nonlinear observer for systems with uncertainties usually requires some sufficient conditions. In this paper we consider a class of systems with two uncertain parts: one which satisfies the Lipschitz condition, whilst the other does not satisfy the Lipschitz condition but is a bounded uncertainty. Sliding mode theory is applied to yield feedforward compensation control to stabilize the error estimation system with and without Lipschitz uncertainty. New sufficient conditions for stability of the Thau observer are proposed. These conditions ensure the stability of the nonlinear observer by selecting a suitable observer gain matrix.