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We consider detection of a current dipole source in the head by magnetoencephalography (MEG) and electroencephalography (EEG) using the fundamental statistical techniques of generalized likelihood ratio (GLR) tests. The distributions of the GLR, under the null hypothesis H/sub 0/ and the alternative H/sub 1/, are estimated in order to find the probabilities of false alarm P/sub fa/ and detection P/sub d/ under a variety of conditions. We also derive a modified version of the GLR test that enables analytical computation of P/sub fa/ and P/sub d/ when the dipole's position is unknown. The results may be applied to compare the detection performance of different MEG/EEG systems and to optimize array design.