Understanding the neural processes underpinning individual differences in early language development is of increasing interest, as it is known to vary in typical development and to be quite heterogeneous in neurodevelopmental conditions. However, few studies to date have tested whether early brain measures are indicative of the developmental trajectory of language, as opposed to language outcomes at specific ages. We combined recordings from two longitudinal studies, including typically developing infants without a family history of autism, and infants with increased likelihood of developing autism (infant‐siblings) ( N = 191). Electroencephalograms (EEG) were recorded at 6 months, and behavioral assessments at 6, 12, 18, 24 and 36 months of age. Using a growth curve model, we tested whether absolute EEG spectral power at 6 months was associated with concurrent language abilities, and developmental change in language between 6 and 36 months. We found evidence of an association between 6‐month alpha‐band power and concurrent, but not developmental change in, expressive language ability in both infant‐siblings and control infants. The observed association between 6‐month alpha‐band power and 6‐month expressive language was not moderated by group status, suggesting some continuity in neural mechanisms.