In this paper, we investigate the ability of Dutch agrammatic Broca's and Wernicke's aphasics to assign reference to possessive pronouns in elided VP constructions. The assumption is that the comprehension problems in these two populations have different sources that are revealed in distinct patterns of responses. The focus is primarily on the performance of the agrammatic group whose errors in comprehension are not viewed as a consequence of a breakdown of grammatical knowledge but as a result of limited processing resources (for an overview see Grodzinsky, 2000). The results of the present study provide evidence for the psycholinguistic reality of the economy hierarchy as proposed in the Primitives of Binding (Reuland, 2001). According to the economy hierarchy proposed for the non-brain-damaged, the more economical semantic dependencies are preferred over the costlier discourse dependencies. This hierarchy is reflected in agrammatic aphasia where the semantic dependencies are available on time and preferred over the discourse dependences that are not available on time as a result of the lack of processing resources with consequences for comprehension.