Children with preschool language difficulties are at high risk of literacy problems; however, the nature of the relationship between delayed language development and dyslexia is not understood. Three hundred eight Slovak and Czech children were recruited into three groups: family risk of dyslexia, speech/language difficulties and controls, and were assessed three times from kindergarten until Grade 1. There was a twofold increase in probability of reading problems in each risk group. Precursors of ‘dyslexia’ included difficulties in oral language and code‐related skills (phoneme awareness, letter‐knowledge and rapid automatized naming); poor performance in phonological memory and vocabulary was observed in both affected and unaffected high‐risk peers. A two‐group latent variable path model shows that early language skills predict code‐related skills, which in turn predict literacy skills. Findings suggest that dyslexia in Slavic languages has its origins in early language deficits, and children who succumb to reading problems show impaired code‐related skills before the onset of formal reading instruction. Copyright © 2016 John Wiley & Sons, Ltd.