This paper describes the results of a significant research and development effort conducted at NASA Ames Research Center to develop new text mining algorithms to discover anomalies in free-text reports regarding system health and safety of two aerospace systems. We discuss two problems of significant import in the aviation industry. The first problem is that of automatic anomaly discovery concerning an aerospace system through the analysis of tens of thousands of free-text problem reports that are written about the system. The second problem that we address is that of automatic discovery of recurring anomalies, i.e., anomalies that may be described in different ways by different authors, at varying times and under varying conditions, but that are truly about the same part of the system. The intent of recurring anomaly identification is to determine project or system weakness or high-risk issues. The discovery of recurring anomalies is a key goal in building safe, reliable, and cost-effective aerospace systems.