The three classical process algebra CCS, CSP and ACP present several differences in their respective technical machinery. This is due, not only to the difference in their operators, but also to the terminology and “way of thinking” of the community which has been (and still is) working with them. In this paper we will first discuss such differences and try to clarify the different usage of terminology and concepts. Then, as a result of this discussion, we define a generic process algebra where each basic mechanism of the three process algebras is expressed by an operator and which can be used as an underlying common language. We show an example of the advantages of adopting such a language instead of one of the three more specialized algebras: producing a complete axiomatization of finite-state behaviours.