Object-oriented analysis and design methodologies take full advantage of the object approach when it comes to modeling the objects in a system. However, system behavior continues to be modeled using essentially the same tools as in traditional systems analysis: state diagrams and dataflow diagrams. In this paper we extend the notion of specialization to these process representations and identify a set of transformations which, when applied to a process description, always result in specialization. We analyze specific examples in detail and demonstrate that such a use of specialization is not only theoretically possible, but shows promise as a method for categorizing and analyzing processes. We identify a number of apparent inconsistencies between process specialization and the object specialization which is part of the object-oriented approach. We demonstrate that these apparent inconsistencies are superficial and that the approach we take is compatible with the traditional notion of specialization.