In the human brain, the alpha rhythm in occipital cortex and the mu rhythm in sensorimotor cortex are among the most prominent rhythms, with both rhythms functionally implicated in gating modality-specific information. Separation of these rhythms is non-trivial due to the spatial mixing of these oscillations in sensor space. Using a computationally efficient processing pipeline requiring no manual data cleaning, we isolated alpha and/or mu rhythms from electroencephalography recordings performed on 1605 children aged 5-18. Using the extracted time series for each rhythm, we characterized the waveform shape on a cycle-by-cycle basis and examined whether and how the waveform shape differs across development. We demonstrate that alpha and mu rhythms both exhibit nonsinusoidal waveform shape that changes significantly across development, in addition to the known large changes in oscillatory frequency. This dataset also provided an opportunity to assess oscillatory measures for attention-deficit hyperactivity disorder (ADHD) and autism spectrum disorder (ASD). We found no differences in the resting-state features of these alpha-band rhythms for either ADHD or ASD in comparison to typically developing participants in this dataset. While waveform shape is ignored by traditional Fourier spectral analyses, these nonsinusoidal properties may be informative for building more constrained generative models for different types of alpha-band rhythms, yielding more specific insight into their generation.