The present paper defines ST-structures (and an extension of these, called STC-structures). The main purpose is to provide concrete relationships between highly expressive concurrency models coming from two different schools of thought: the higher dimensional automata, a \textit{state-based} approach of Pratt and van Glabbeek; and the configuration structures and (in)pure event structures, an \textit{event-based} approach of van Glabbeek and Plotkin. In this respect we make comparative studies of the expressive power of ST-structures relative to the above models. Moreover, standard notions from other concurrency models are defined for ST(C)-structures, like steps and paths, bisimilarities, and action refinement, and related results are given. These investigations of ST(C)-structures are intended to provide a better understanding of the \textit{state-event duality} described by Pratt, and also of the (a)cyclic structures of higher dimensional automata.