Phonological constancy refers to infants’ ability to disregard variations in the phonetic realisation of speech sounds that do not indicate lexical contrast, e.g., when listening to accented speech. In typically-developing infants, this ability develops between 15- and 19-months of age, coinciding with the consolidation of infants’ native phonological competence and vocabulary growth. Here we investigated the developmental time course of phonological constancy in infants at family risk for developmental dyslexia, using a longitudinal design. Developmental dyslexia is a disorder affecting the acquisition of reading and spelling skills, and it also affects early auditory processing, speech perception, and lexical acquisition. Infants at-risk and not at-risk for dyslexia, based on a family history of dyslexia, participated when they were 15-, 19-, and 26-months of age. Phonological constancy was indexed by comparing at-risk and not at-risk infants’ ability to recognise familiar words in two preferential looking tasks: (1) a task using words presented in their native accent, and (2) a task using words presented in a non-native accent. We expected a delay in phonological constancy for the at-risk infants. As predicted, in the non-native accent task, not at-risk infants recognised familiar words by 19 months, but at-risk infants did not. The control infants thus exhibited phonological constancy. By 26 months, at-risk toddlers did show successful word recognition in the native accent task. However, for the non-native accent task at 26 months, neither at-risk nor control infants showed familiar word recognition. These findings are discussed in terms of the impact of family risk for dyslexia on toddlers’ consolidation of early phonological and lexical skills.