In this paper, the fault diagnosis problem for a class of non-linear systems with uncertainty which depends on states, inputs and unknown constant parameters is discussed. Under some geometric conditions, the system is transformed into two different subsystems. One is not affected by actuator faults, so a non-linear adaptive observer can be designed based on the assumption of the strictly positive realness (SPR). The other whose states can be measured is affected by the faults. Actuator fault diagnosis is based on estimations of both the state and the unknown parameters with good accuracy. Discussions on release of SPR requirement and extension to the sensor fault case are also made. Finally, two examples are given in order to illustrate the applicability of the proposed methods for actuator fault diagnosis and sensor fault diagnosis respectively.