The study of electroencephalographic (EEG) activity during sleep in the spider monkey has provided new insights into primitive arboreal sleep physiology and behavior in anthropoids. Nevertheless, studies conducted to date have maintained the frequency ranges of the EEG bands commonly used with humans. The aim of the present work was to determine the EEG broad bands that characterize sleep and wakefulness in the spider monkey using principal component analysis (PCA). The EEG activity was recorded from the occipital, central, and frontal EEG derivations of six young‐adult male spider monkeys housed in a laboratory setting. To determine which frequencies covaried and which were orthogonally independent during sleep and wakefulness, the power EEG spectra and interhemispheric and intrahemispheric EEG correlations from 1 to 30 Hz were subjected to PCA. Findings show that the EEG bands detection differed from those reported previously in both spider monkeys and humans, and that the 1–3 and 2–13 Hz frequency ranges concur with the oscillatory activity elucidated by cellular recordings of subcortical regions. Results show that applying PCA to the EEG spectrum during sleep and wakefulness in the spider monkey led to the identification of frequencies that covaried with, and were orthogonally independent of, other frequencies in each behavioral vigilance state. The new EEG bands differ from those used previously with both spider monkeys and humans. The 1–3 and 2–13 Hz frequency ranges are in accordance with the oscillatory activity elucidated by cellular recordings of subcortical regions in other mammals.