We introduce iteration in process algebra by means of (the original, binary version of) Kleene's star operation: x * y is the process that chooses between x and y, and upon termination of x has this choice again. We add this operation to a whole range of process algebra axiom systems, starting from BPA (Basic Process Algebra). In the case of the most complex system under consideration, ACP τ , every regular process can be defined with handshaking (two-party communication) and auxiliary actions. Next we introduce nesting in process algebra: x#y is defined by the equation x#y=x(x#y)x+y