This study examines whether phonological and nonphonological cognitive tasks predict reading acquisition in Greek. Planning, attention, simultaneous processing, and successive processing tasks together with three phonological coding tasks (alliteration, phoneme elision, and sound isolation) were administered to 50 Greek and 50 Cypriot Grade 1 students. Word Attack and Word Identification were administered to measure early reading competency. Given that Cyprus uses a whole-language approach and Greece a phonic approach, results examine the role of phonological and nonphonological cognitive tasks in predicting reading acquisition under two contrasting instructional systems. Discussion focuses on early predictors of reading development under different instructional conditions.