This paper presents a new method for localizing the electric activity in the brain based on multichannel surface EEG recordings. In contrast to the models presented up to now the new method does not assume a limited number of dipolar point sources nor a distribution on a given known surface, but directly computes a current distribution throughout the full brain volume. In order to find a unique solution for the 3-dimensional distribution among the infinite set of different possible solutions, the method assumes that neighboring neurons are simultaneously and synchronously activated. The basic assumption rests on evidence from single cell recordings in the brain that demonstrates strong synchronization of adjacent neurons. In view of this physiological consideration the computational task is to select the smoothest of all possible 3-dimensional current distributions, a task that is a common procedure in generalized signal processing. The result is a true 3-dimensional tomography with the characteristic that localization is preserved with a certain amount of dispersion, i.e., it has a relatively low spatial resolution. The new method, which we call Low Resolution Electromagnetic Tomography (LORETA) is illustrated with two different sets of evoked potential data, the first showing the tomography of the P100 component to checkerboard stimulation of the left, right, upper and lower hemiretina, and the second showing the results for the auditory N100 component and the two cognitive components CNV and P300. A direct comparison of the tomography results with those obtained from fitting one and two dipoles illustrates that the new method provides physiologically meaningful results while dipolar solutions fail in many situations. In the case of the cognitive components, the method offers new hypotheses on the location of higher cognitive functions in the brain.