Relational structures based on acyclic orders can successfully model a fundamental class of concurrent system behaviours. We have exemplified this by considering concurrency traces and en-systems. However, there are important cases, such as en-systems with activator arcs, where more general relational structures are needed. In this chapter, we present a general theory of relational structures which can be used to model concurrent behaviours as well as specific frameworks for dealing with behaviours generated by execution models based on step sequence executions.