This study examines the development of the narrative competence, from the analysis of the structure of narratives of personal experience on accidents. The theoretical sustenance is based on the sociolinguistic approaches on the analysis of the oral narratives and the contributions of the psycholinguistics to the study of the narratives of personal experience in the infantile speech. The sample is shaped by 60 narratives by 5, 9 and 11-year-old children (boys and girls). It is observed that the oldest children produce more complex statements, as for their elaboration