In this talk I will discuss results of research conducted in collaboration with Iain Raeburn. Our work concerns the general problem of constructing and analyzing C*-algebras built from irreversible dynamical systems. We are particularly interested in how to describe those C*-algebras that are built from two commuting local homeomorphisms. We use so-called Exel systems, which are a certain type of product system that has appeared in the literature. I will explain how the canonical transfer operators associated to the local homeomorphisms may be used to build the product systems and how product sys- tems, in turn, lead to the C*-algebras. A key concept is the notion of *-commuting local homeomorphisms. I will explore this notion and indicate its impact on the structure of the C*-algebras.