Slow cortical oscillations play a crucial role in processing the speech envelope, which is perceived atypically by children with Developmental Language Disorder (DLD) and developmental dyslexia. Here we use electroencephalography (EEG) and natural speech listening paradigms to identify neural processing patterns that characterize dyslexic versus DLD children. Using a story listening paradigm, we show that atypical power dynamics and phase-amplitude coupling between delta and theta oscillations characterize dyslexic and DLD children groups, respectively. We further identify EEG common spatial patterns (CSP) during speech listening across delta, theta and beta oscillations describing dyslexic versus DLD children. A linear classifier using four delta-band CSP variables predicted dyslexia status (0.77 AUC). Crucially, these spatial patterns also identified children with dyslexia in a rhythmic syllable task EEG, suggesting a core developmental deficit in neural processing of speech rhythm. These findings suggest that there are distinct atypical neurocognitive mechanisms underlying dyslexia and DLD.