The authors propose a specific characteristics framework in order to construct linkages between alternative approaches to modeling product differentiation. It is shown that a demand system that satisfies the gross substitutes property imposes specific requirements on the locations of products. In particular, the dimension of the characteristics space must be larger than, or equal to, the number of products minus one. The authors then identify a method for casting a given demand system into their characteristics framework. This is illustrated for the logit, probit, and linear probability models of discrete choice theory. Finally, the authors find a characteristics representation of the CES representative consumer. Copyright 1989 by The Review of Economic Studies Limited.