We propose a specific characteristics framework in order to construct linkages between alternative conceptual approaches to modelling product differentiation. First, it is shown that a demand system which 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. We then identify a method for casting a given demand system (subject to certain restrictions) into our characteristics framework. This is illustrated for the logit, probit and linear probability models of discrete choice theory. Finally, we find a characteristics representation of the CES representative consumer.