Here we use two filtered speech tasks to investigate children's processing of slow (<4 Hz) versus faster (∼33 Hz) temporal modulations in speech. We compare groups of children with either developmental dyslexia (Experiment 1) or speech and language impairments (SLIs, Experiment 2) to groups of typically-developing (TD) children age-matched to each disorder group. Ten nursery rhymes were filtered so that their modulation frequencies were either low-pass filtered (<4 Hz) or band-pass filtered (22 - 40 Hz). Recognition of the filtered nursery rhymes was tested in a picture recognition multiple choice paradigm. Children with dyslexia aged 10 years showed equivalent recognition overall to TD controls for both the low-pass and band-pass filtered stimuli, but showed significantly impaired acoustic learning during the experiment from low-pass filtered targets. Children with oral SLIs aged 9 years showed significantly poorer recognition of band pass filtered targets compared to their TD controls, and showed comparable acoustic learning effects to TD children during the experiment. The SLI samples were also divided into children with and without phonological difficulties. The children with both SLI and phonological difficulties were impaired in recognizing both kinds of filtered speech. These data are suggestive of impaired temporal sampling of the speech signal at different modulation rates by children with different kinds of developmental language disorder. Both SLI and dyslexic samples showed impaired discrimination of amplitude rise times. Implications of these findings for a temporal sampling framework for understanding developmental language disorders are discussed.