This paper describes research toward developing prognostics technologies for light water nuclear power reactor components. The focus of this paper is on passive components (those that do not need to change state or move to perform their function), although the technologies are applicable to other classes of components as well. A prototypic failure mechanism (high-cycle fatigue) is used to focus the efforts and provide context for the development effort. A Bayesian framework is proposed for the prognostics of remaining useful life and applied to simulated data sets representing nondestructive measurements of high-cycle fatigue damage. The initial results of the prognostics based on simulated data sets are presented.