The observer design problem is studied for a class of multi-output nonlinear systems that are not necessarily observable. Generalized nonlinear observer canonical form is introduced for multi-output nonlinear systems to design nonlinear observers. Sufficient conditions are given for a nonlinear system to be transformed by state-space change of coordinates into generalized nonlinear observer canonical form. Based on this canonical from, a sufficient condition is also given for the existence of nonlinear observers. An illustrative example is presented to show the design procedure of the proposed method.