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This article studies the problem of transforming a process model with an arbitrary topology into an equivalent well-structured process model. While this problem has received significant attention, there is still no full characterization of the class of unstructured process models that can be transformed into well-structured ones, nor an automated method for structuring any process model that belongs to this class. This article fills this gap in the context of acyclic process models. The article defines a necessary and sufficient condition for an unstructured acyclic process model to have an equivalent well-structured process model under fully concurrent bisimulation, as well as a complete structuring method. The method has been implemented as a tool that takes process models captured in the BPMN and EPC notations as input. The article also reports on an empirical evaluation of the structuring method using a repository of process models from commercial practice.