The widespread adoption of graphical notations for software design has created a demand for formally-based methods to support and extend their use. A principal focus for this demand is the Unified Mo- deling Language (UML), and, within UML, the diagrammatic notations for describing dynamic properties. This paper shows how one such notation, that of Activity Graphs, can be given a process semantics in the language of Communicating Sequen- tial Processes (CSP). Such a semantics can be used to demonstrate the consistency of an object model and to provide a link to other methods and tools. A small example is included.