Purpose: To explore the sensitivity of children with specific language impairment (SLI) to amplitude-modulated and durational cues that are important for perceiving suprasegmental speech rhythm and stress patterns. Method: Sixty-three children between 7 and 11 years of age were tested, 21 of whom had a diagnosis of SLI, 21 of whom were matched for chronological age to the SLI sample, and 21 of whom were matched for language age to the SLI sample. All children received a battery of nonspeech auditory processing tasks along with standardized measures of phonology and language. Results: As many as 70%-80% of children diagnosed with SLI were found to perform below the 5th percentile of age-matched controls in auditory processing tasks measuring sensitivity to amplitude envelope rise time and sound duration. Furthermore, individual differences in sensitivity to these cues predicted unique variance in language and literacy attainment, even when age, nonverbal IQ, and task-related (attentional) factors were controlled. Conclusion: Many children with SLI have auditory processing difficulties, but for most children, these are not specific to brief, rapidly successive acoustic cues. Instead, sensitivity to durational and amplitude envelope cues appear to predict language and literacy outcomes more strongly. This finding now requires replication and exploration in languages other than English.