In this paper, the fault diagnosis problem for a class of nonlinear multiple-input multiple-output (MIMO) systems with uncertainty is investigated. Under some geometric conditions, the system is transformed into two different subsystems. One is in the generalized observer canonical form and is not affected by actuator faults, so a nonlinear sliding mode observer for this subsystem is constructed. The other whose states can be measured is affected by the faults. The observation scheme is then used for actuator fault identification with good accuracy. Extension to sensor fault diagnosis is also made. Finally, a numerical example is used to illustrate the efficiency of the proposed method.