We investigated spatial properties of the source distributions that generate scalp electroencephalographic (EEG) oscillations. The inherent complexity of the spatio-temporal dynamics of EEG oscillations indicates that conceptual models that view source activity as consisting only of a few "equivalent dipoles" are inadequate. We present an approach that uses volume conduction models to characterize the distinct spatial filtering of cortical source activity by average reference EEG, high-resolution EEG, and magnetoencephalography (MEG). By comparing these three measures, we can make inferences about the sources of EEG oscillations without having to make prior assumptions about the sources. We apply this approach to spontaneous EEG oscillations observed with eyes closed at rest. Both EEG and MEG recordings show robust alpha rhythms over posterior regions of the cortex; however, the dominant frequency of these rhythms varies between EEG and MEG recordings. Frontal alpha and theta rhythms are generated almost exclusively by superficial radial dipole layers that generate robust EEG signals but very little MEG signals; these sources are presumably mainly in the gyral crowns of frontal cortex. MEG and high-resolution EEG estimates of alpha rhythms provide evidence of local tangential and radial sources in the posterior cortex, lying mainly on sulcal and gyral surfaces. Despite the detailed information about local radial and tangential sources potentially afforded by high-resolution EEG and MEG, it is also evident that the alpha and theta rhythms receive contributions from non-local source activity, for instance large dipole layers distributed over lobeal or (potentially) even larger spatial scales.