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Although it is common in large Java programs to rethrow exceptions, existing exception-flow analyses find only single exception-flow links, thus are unable to identify multiple-link exception propagation paths. This paper presents a new static analysis that, when combined with previous exception-flow analyses, computes chains of semantically-related exception-flow links, and thus reports entire exception propagation paths, instead of just discrete segments of them. These chains can be used 1) to show the error handling architecture of a system, 2) to assess the vulnerability of a single component and the whole system, 3) to support better testing of error recovery code, and 4) to facilitate the tracing of the root cause of a logged problem. Empirical findings and a case history for Tomcat show that a significant portion of the chains found in our benchmarks span multiple components, and thus are hard to find manually.