This paper provides a further investigation into the linguistic abilities of a subgroup of 12 Grammatical specific language impaired (SLI) children (aged 10;2 to 13;11). The study investigates the use of referential expressions (e.g. pronouns) in a narrative discourse, and provides insight into the underlying nature of Grammatical SLI, thereby contributing to the modularity debate. Previous investigations indicate that Grammatical SLI children have a deficit with dependent structural relationships, i.e. a Representational Deficit for Dependent Relationships (RDDR). Grammatical SLI children's RDDR appears to be a modular language deficit. To test this claim, linguistic representations of dependent structural relationships which are not part of the modular language system are investigated using a narrative discourse based on the picture book Frog where are you? The SLI children's pattern of referential expressions was compared with 36 language ability controls (aged 6;4 to 9;8). The findings indicated that the Grammatical SLI children have relatively mature linguistic development in the use of referential expressions to produce a cohesive, structured narrative discourse. The view of the organisation of the mind in which a modular language system can be differentially impaired from aspects of language which rely on the central system can most easily account for the data. Thus, the data support the hypothesized modular nature of Grammatical SLI children's underlying linguistic deficit. The implications of the findings for language acquisition are discussed.