<div>We present an axiom system ACP, for communicating processes with silent actions (‘&tau;-steps’). The system is an extension of ACP, Algebra of Communicating Processes, with Milner's &tau;-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for ACP_&tau;, syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACP_&tau;. Finally, termination of rewriting terms according to the ACP_&tau;, axioms is probed using the method of recursive path orderings.</div>