Nonparametric statistical testing of EEG and MEG data is presented, offering a flexible approach to analyze these signals without assuming a specific distribution. The method addresses the multiple comparisons problem (MCP) by controlling the family-wise error rate (FWER) through a permutation test. This test involves randomly partitioning data and calculating a test statistic based on the distribution of these partitions. The p-value is derived from the proportion of random partitions yielding a test statistic greater than the observed one. This approach is nonparametric, allowing for biophysically motivated constraints to enhance sensitivity. The paper is written for two audiences: empirical neuroscientists seeking practical methods and methodologists interested in theoretical foundations. It explains how nonparametric tests formally control the false alarm rate under the null hypothesis of identical distributions. The method is demonstrated using an example of semantic processing, where the N400 effect is analyzed. The nonparametric test is shown to be effective in both single-sensor and multi-sensor analyses, as well as in oscillatory activity studies. The test is validated by showing that it maintains the correct false alarm rate under the null hypothesis, making it a robust solution for MEEG data analysis.Nonparametric statistical testing of EEG and MEG data is presented, offering a flexible approach to analyze these signals without assuming a specific distribution. The method addresses the multiple comparisons problem (MCP) by controlling the family-wise error rate (FWER) through a permutation test. This test involves randomly partitioning data and calculating a test statistic based on the distribution of these partitions. The p-value is derived from the proportion of random partitions yielding a test statistic greater than the observed one. This approach is nonparametric, allowing for biophysically motivated constraints to enhance sensitivity. The paper is written for two audiences: empirical neuroscientists seeking practical methods and methodologists interested in theoretical foundations. It explains how nonparametric tests formally control the false alarm rate under the null hypothesis of identical distributions. The method is demonstrated using an example of semantic processing, where the N400 effect is analyzed. The nonparametric test is shown to be effective in both single-sensor and multi-sensor analyses, as well as in oscillatory activity studies. The test is validated by showing that it maintains the correct false alarm rate under the null hypothesis, making it a robust solution for MEEG data analysis.