Modern industry is concerned about extending the lifetime of its critical processes and maintaining them only when required. Significant aspects of these trends include the ability to diagnose impending failures, prognosticate the remaining useful lifetime of the process and schedule maintenance operations so that uptime is maximized. Prognosis is probably the most difficult of the three issues leading to condition-based maintenance (CBM). This paper attempts to address this challenging problem with intelligence-oriented techniques, specifically dynamic wavelet neural networks (DWNNs). DWNNs incorporate temporal information and storage capacity into their functionality so that they can predict into the future, carrying out fault prognostic tasks. Such fundamental issues as the network structure, learning algorithms, stability analysis, uncertainty management, and performance assessment are studied in a theoretical framework. An example is presented in which a trained DWNN successfully prognoses a defective bearing with a crack in its inner race.