This paper addresses the question whether the cognitive underpinnings of reading and spelling are universal or whether there are language/orthography-specific differences. We analysed concurrent predictions of phonological processing (awareness and memory) and rapid automatized naming (RAN) for literacy development in a large (N = 1062) European sample of typically developing elementary school children beyond Grade 2 acquiring five different alphabetic orthographies with varying degrees of grapheme-phoneme consistency (English, French, German, Hungarian, Finnish). Findings indicate that (1) phonological processing and RAN constitute two separate factors which both account for significant amounts of unique variance in literacy attainment in all five orthographies. Associations of these proximal predictor measures with reading speed, reading accuracy, and spelling are differential: in general, RAN was the best predictor of reading speed while phonological processing accounted for higher amounts of unique variance in reading accuracy and spelling; (2) the predictive patterns were largely comparable across orthographies, with two exceptions: first the overall predictive power of the cognitive skills on literacy measures was higher in English than in more consistent orthographies and secondly, RAN tended to account for more variance in reading accuracy and spelling in English than in all other orthographies.