A novel approach is presented for the fault detection and diagnosis (FDD) of faults in actuators and sensors via the use of adaptive updating rules. The system considered is linear time-invariant and is subjected to an unknown input that represents either model uncertainty or unmeasurable disturbances. First, fault detection and diagnosis for linear actuators and sensors is considered, where a fixed observer is used to detect the fault whilst an adaptive diagnositic observer is constructed to diagnose the fault. Using the augmented error technique from model reference adaptive control, an observation error model is formulated and used to establish an adaptive diagnostic algorithm that produces an estimate of the gains of actuator and the sensor. An extension to the fault detection and diagnosis to cover nonlinear actuators is also made, where a similar augmented error model to that used for linear actuators and sensors is obtained. As a result, a convergent adaptive diagnostic algorithm for estimating the parameters in the nonlinear actuators is developed. Two simulated numerical examples are included to demonstrate the use of the proposed approaches.