In this paper we present preliminary results of a rigorous development of the actor model of computation. We present an actor language which is an extension of a simple functional language, and provide a precise operational semantics for this extension. Our actor systems are open distributed systems, meaning we explicitly take into account the interface with external components in the specification of an actor system. We define and study various notions of equivalence on actor expressions and systems. We show that the usual tripartite family of testing equivalence relations collapses to two in the presence of fairness. We define a notion of operational bisimulation as a tool for establishing equivalence under fairness assumptions, and illustrate its use.