We describe a method to detect brain activation in cortically constrained maps of current density computed from magnetoencephalography (MEG) data using multivariate statistical inference. We apply time–frequency (wavelet) analysis to individual epochs to produce dynamic images of brain signal power on the cerebral cortex in multiple time–frequency bands. We form vector observations by concatenating the power in each frequency band, and fit them into separate multivariate linear models for each time band and cortical location with experimental conditions as predictor variables. The resulting Roy's maximum root statistic maps are thresholded for significance using permutation tests and the maximum statistic approach. A source is considered significant if it exceeds a statistical threshold, which is chosen to control the familywise error rate, or the probability of at least one false positive, across the cortical surface. We compare and evaluate the multivariate approach with existing univariate approaches to time–frequency MEG signal analysis, both on simulated data and experimental data from an MEG visuomotor task study. Our results indicate that the multivariate method is more powerful than the univariate approach in detecting experimental effects when correlations exist between power across frequency bands. We further describe protected F-tests and linear discriminant analysis to identify individual frequencies that contribute significantly to experimental effects. Hum Brain Mapp, 2009. © 2009 Wiley-Liss, Inc.