In this paper, we present a state observer for a class of nonlinear systems based on the input output linearization, While the previous result presented state observers for nonlinear systems of full relative degree, we proposed a procedure for the design of nonlinear state observers which do not require the hypothesis of full relative degree. Assuming that there exists a global state observer for internal dynamics and that some functions are globally Lipschitz, we can design a globally convergent state observer. It is also shown that if the zero dynamics are locally exponentially stable, then there exists a local state observer. An example is gi, en to illustrate the proposed design of nonlinear state observers.