Graph oriented models are at the core of most business process management systems. In recent years, “algebraic” business process modeling languages based on different process calculi have been proposed. The semantics of these algebraic process languages are quite different, and seemingly incompatible, with those of graph oriented approaches. In this paper we study how the BPEL4WS exception handling mechanism is used to integrate the algebraic and graph process models. Unlike other approaches to exception handling in business processes, the BPEL4WS model does not require that the process topology be constrained by the exception handling hierarchy, thus allowing both highly structured and graph based processes to benefit from it. Based on this exception handling model, we explain “dead path elimination” (the runtime mechanism by which process termination is ensured) as a form of exception processing. The integration of dead path elimination with the exception handling mechanism provides the semantic base for the integration of the graph and algebraic processes models in BPEL4WS.