Since event-related components in MEG (magnetoencephalography) studies are often buried in background brain activity and environmental and sensor noise, it is a standard technique for noise reduction to average over multiple stimulus-locked responses or "epochs". However this also removes event-related changes in oscillatory activity that are not phase locked to the stimulus. To overcome this problem, we combine time-frequency analysis of individual epochs with cortically-constrained imaging to produce dynamic images of brain activity on the cerebral cortex in multiple time-frequency bands. While the SNR in individual epochs is too low to see any but the strongest components, we average signal power across epochs to find event related components on the cerebral cortex in each frequency band. To determine which of these components are statistically significant within an individual subject, we threshold the cortical images to control for false positives. This involves testing thousands of hypotheses (one per surface element and time-frequency band) for signif-icant experimental effects. To control the number of false positives over all tests, we must therefore apply multiplicity adjustments by controlling the familywise error rate, i.e. the probability of one or more false positive detections across the entire cortex. Applying this test to each frequency band produces a set of cortical images showing significant event-related activity in each band of interest. We demonstrate this method in applications to high density MEG studies of visual attention.