A study was conducted to examine congruence relations of EEG frequency factors between hemispheres. The central questions were aimed at procedural details of the factoring process which have the greatest "destructive" influence on congruence of factor patterns. On the basis of serially-rotated oblique solutions and evaluative simple structure criteria, two methodological results are reported: (a) the original principal components of two lead placements show a marked departure from an ideal congruence pattern, but can be forced into high congruence beyond 0.90 for the first twelve components by orthogonal procrustes rotation; (b) after this matching of principal components the expected optimum of congruence is only achieved in rotated solutions showing an optimal simple structure in terms of the Index of Factorial Simplicity (Kaiser, 1974). Additionally, the study leads to two substantive electroencephalographic results; (c) the factorial frequency structure of spontaneous EEG from two homologous positions (C3, C4) of the hemispheres is highly congruent. Thus, an identical measurement rationale for EEG frequency bands can be justified in asymmetry research; (d) the spectral dimensions of the alpha region show good correspondence to a recently published synoptic model of factor analytically defined EEG bands (Andresen, Thom, Irrgang, & Stemmler, 1982). The weight system of the three alpha components in this model can be recommended for psychophysiologically oriented EEG research.