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A statistical frequency domain approach to localizing equivalent dipole generators of human brain evoked potentials is described. The frequency domain representation allows considerable data reduction, constrains the magnitude function of the dipoles to be smooth, and accounts for the statistical properties of the background EEG. A general model in which dipole orientation can vary over time, and which includes multiple dipole generators is considered. The varying orientation model has the practical advantage of being more nearly linear and more flexible than a fixed orientation model, which facilitates convergence of the iterative fitting algorithm. A measure of goodness-of-fit that compares the likelihood of the dipole model with the likelihoods of saturated and null models is suggested. The results of fitting the model report recorded auditory and visual evoked potentials are reported. A single dipole with fixed orientation seems to be an adequate model of the auditory midlatency response, while two dipoles with varying orientation are needed to fit the later P200 component. Analysis of the visual P100 response to unilateral stimulation localized a generator in the contralateral occipital cortex, as expected from anatomical considerations.