This paper reports an investigation of the knowledge of binding in young adults with Down syndrome (DS), speakers of Serbo-Croatian, and compares it to that of English-speaking individuals with DS and typically developing controls. In line with data reported for English, Serbo-Croatian speakers with DS showed difficulties interpreting anaphoric elements. It is argued that these results point to a specific deficit in the grammar of DS: an inability to establish a syntactic relationship of binding between an anaphor and its antecedent. These results present evidence against the characterisation of language development in DS as delayed, since the pattern observed in this population cross-linguistically has not been observed during any stage of typical language development.