This longitudinal study investigated temporal auditory processing (frequency modulation and between-channel gap detection) and speech perception (speech-in-noise and categorical perception) in three groups of 6 years 3 months to 6 years 8 months-old children attending grade 1: (1) children with specific language impairment (SLI) and literacy delay (n = 8), (2) children with SLI and normal literacy (n = 10) and (3) typically developing children (n = 14). Moreover, the relations between these auditory processing and speech perception skills and oral language and literacy skills in grade 1 and grade 3 were analyzed. The SLI group with literacy delay scored significantly lower than both other groups on speech perception, but not on temporal auditory processing. Both normal reading groups did not differ in terms of speech perception or auditory processing. Speech perception was significantly related to reading and spelling in grades 1 and 3 and had a unique predictive contribution to reading growth in grade 3, even after controlling reading level, phonological ability, auditory processing and oral language skills in grade 1. These findings indicated that speech perception also had a unique direct impact upon reading development and not only through its relation with phonological awareness. Moreover, speech perception seemed to be more associated with the development of literacy skills and less with oral language ability. (Contains 1 figure and 4 tables.)