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The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism of structured occurrence nets has been introduced to facilitate the portrayal and analysis of the behaviours, and in particular failures, of complex evolving systems. Such systems are composed of a large number of sub-systems which may proceed concurrently and interact with each other and with the external environment while their behaviour is subject to modification by other systems. The purpose of this paper is to provide an extension of structured occurrence nets to include models built up of acyclic nets rather than occurrence nets.