Children with specific language impairments (SLIs) show impaired perception and production of spoken language, and can also present with motor, auditory and phonological difficulties. Recent auditory studies have shown impaired sensitivity to amplitude rise time (ART) in children with SLIs, along with non-speech rhythmic timing difficulties. Linguistically, these perceptual impairments should affect sensitivity to speech prosody and syllable stress. Here we used two tasks requiring sensitivity to prosodic structure, the DeeDee task and a stress misperception task, to investigate this hypothesis. We also measured auditory processing of ART, rising pitch and sound duration, in both speech (ba) and non-speech (tone) stimuli. Participants were 45 children with SLI aged on average 9 years and 50 age-matched controls. We report data for all the SLI children (N = 45, IQ varying), as well as for two independent SLI subgroupings with intact IQ. One subgroup, Pure SLI, had intact phonology and reading (N=16), the other, SLI PPR (N=15), had impaired phonology and reading. Problems with syllable stress and prosodic structure were found for all the group comparisons. Both sub-groups with intact IQ showed reduced sensitivity to ART in speech stimuli, but the PPR subgroup also showed reduced sensitivity to sound duration in speech stimuli. Individual differences in processing syllable stress were associated with auditory processing. These data support a new hypothesis, the ‘prosodic phrasing’ hypothesis, which proposes that grammatical difficulties in SLI may reflect perceptual difficulties with global prosodic structure related to auditory impairments in processing amplitude rise time and duration.