Procedures are advanced in the thesis for analysing the semigroup representation of structure in systems of social relations. Such systems may consist of multiple, social networks (Lorrain, 1975; Lorrain and White, 1971) or of blockmodels derived from multirelational network data (Boorman and White, 1976; White, Boorman and Breiger, 1976). The aim of the proposed analysis is to clarify the nature of the representation, as well as to enhance its potential usefulness, by making explicit the relational features upon which it depends. An underlying purpose is therefore also a general evaluative one. (For complete abstract open document.)