We consider the generic hypermedia structure of a document to be a means of representing the document that allows it to be processed into a wide variety of presentations. Representing a document in this manner requires additional specification and resources to render it into any presentation. In this paper we discuss the relationship between the generic hypermedia structure of documents and the processing of this structure into presentation. Our discussion is expressed in terms of existing models for hypertext and hypermedia systems and also in terms of ISO standards for text and hypermedia document formatting and processing. The discussion and the resulting formalisms and the resulting formalisms are illustrated with extension designs for the hypermedia authoring and presentation environment developed at our laboratory.