This study aimed to describe the process of construction of narrative speech in children with Down`s Syndrome, by showing the existing characteristics in narrative, relating Labov`s structural perspective (1972) to perroni`s interactional pespective (1992), comprehending, this way, the processes that compox the ability of speech of people with Down`s Syndrome and the similarities and differences that exist between personal reports and stories. Students with Down`s Syndrome, aging between 8-12 years old and enrolled at Ulisses Pernambucano Special School, where data was collected. This data was transversal, throughout school semester,and collected by video recordings twice a month. The narrative construction of these children was observed in interactive situations in storytelling and self-reporting classrooms. The results show that the structural perspective is not enough for the constructive process found at the analyzed data; however, an interactional perspective allows to understand the richness of the involved processes in the narrative constructions by these children on and on.