An example is given for the application of the COMSTAT algorithm for multimodal factor analysis to EEG power spectral data. The COMSTAT algorithm enlarges Tucker’s three-mode factor analysis to a multimodal one, and improves his algorithm by a least squares solution. The EEG power spectral data from 65 healthy subjects with an occipital rhythm between 8 and 12 Hz were taken. For demonstration purposes we selected three modes, which have been used by other authors: mode 1: 29 frequency classes, In of relative power, in △f = 1.0-Hz steps between 1 and 30 Hz; mode 2: 16 segments, 40 s each, during the two situational vigilance conditions reaction time (RT) and resting (RS), and mode 3: 65 persons. The frequency mode could be described sufficiently by five factors which we called: δF/α1F; υF/α2; β1F/α1F; β2Fβ3F. The factor-loading profiles were similar to those described earlier in independent data. Thus, in the three-mode model we obtained results comparable to those of two-mode models. In the level of 16 situational segments only two factors were extractable. They described the two situations RT, higher vigilance level, and RS, lower vigilance level. In order to demonstrate the changes in factor structure, if a two-mode model is enlarged by a third mode, we used two models for the description of personal (P) variance. When the matrix persons × segments (P × V) was taken, only two factors were extractable. One factor contrasted persons with a high versus a low vigilance level (VL), and was therefore called the ‘vigilance level factor’. The other contrasted persons with high versus low vigilance fluctuation during the RT and RS recording. This factor was called the ‘vigilance dynamics factor’. When the third mode (frequency classes) was added, then the P variance was increased substantially. We selected a four-factor solution for interpretation. The first factor contrasted persons with high versus low α power, and is called the ‘α-power factor’. The second factor contrasted persons with high α power, peak at 9–10 Hz, low δ, and medium β power versus persons with a high δ power, medium α power, peak 8–9 Hz, and low β power. Since the contrast persons describe spectral poles also seen as changes in vigilance, this spectral factor is called the ‘congruent vigilance factor’. The third factor contrasts persons with high α power, peak 9–10 Hz, low δ power, and low β power versus persons with high δ power, medium α power, peak 10–11 Hz, and high β power. Since the contrast persons described spectral poles, also seen as changes in the so-called dissociative vigilance shift, this factor is called the ‘dissociative vigilance factor’. The fourth factor contrasts persons with high versus low dominant α frequency, and is therefore called the ‘α-frequency factor’. On the basis of these data, we formulate the hypothesis that in EEG data from subjects with occipital α-EEG and for the occipital lead, the most important P-variance sources are the α power, the dominant α frequency, and variance due to dynamic changes which can be caused by a shift in vigilance or a dissociative shift in vigilance. The aim of applying our model in EEG data is to describe variance sources in a multidimensional space. The ultimate goal, however, is to arrive at procedures which allow us to keep more natural sources of variance in our models, and not to exclude these variance sources by rigorous selection of subjects.