Demonstratives and possessives integrate the group of Spanish determiners which can appear before the noun as well as after it. In the post-nominal position, another determiner heading the construction is obligatory. Post-nominal demonstratives differ from post-nominal possessives in that the only determiner which the former can appear with is the definite article. In this paper we aim to get across the relationship between the post-nominal element and the determiner that precedes the construction by revising, in detail, the behavior of these elements in the context of nominal ellipsis. Our approach, framed in Distributed Morphology (Halle & Marantz 1993), not only lets us recognize the differences in the determiner that heads the constructions in each case, but it also lets us determine a series of properties in demonstratives and possessives according to their relationship with the elliptical gap and their role as remnant.