The aim of this study was to examine if specific skills that are developed during preschool years could predict the reading performance in the first and second grade of primary school. Two hundred and eighty-seven children participated in this longitudinal study. At the kindergarten level, phonological awareness (PA), rapid automatised naming, phonological short-term memory, auditory processing, motor skills and oral language were evaluated. Reading performance was evaluated in Grades 1 and 2 of the primary school. Results showed that not only total reading performance, but the accuracy and the fluency of reading as well, are predicted in the first grade of school by the PA and the phonological memory scores during kindergarten. Oral language plays the most important role in the prediction of text comprehension. Total reading performance and fluency of reading in the second grade were predicted by the PA and the phonological memory scores. In this grade, the PA, the phonological memory and the copy of shapes seem to be important for the accuracy of reading. Our results suggest that the utilisation of such early evidence through intervention programmes at the preschool age and during the first school years could contribute to the prevention of possible reading problems in school children.