In this note, fault detection techniques based on finite dimensional results are extended and applied to a class of infinite dimensional dynamical systems. This special class of systems assumes linear plant dynamics having an abrupt additive perturbation as the fault. This fault is assumed to be linear in the (unknown) constant (and possibly functional) parameters. An observer-based model estimate is proposed which serves to monitor the system's dynamics for unanticipated failures, and its well posedness is summarized. Using a Lyapunov synthesis approach extended and applied to infinite dimensional systems, a stable adaptive fault diagnosis (fault parameter learning) scheme is developed. The resulting parameter adaptation rule is able to “sense” the instance of the fault occurrence. In addition, it identifies the fault parameters using the additional assumption of persistence of excitation. Extension of the adaptive monitoring scheme to incipient faults (time varying faults) is summarized. Simulations studies are used to illustrate the applicability of the theoretical results.