The article shows how EEG and MEG data can be analyzed using nonparametric statistical tests. These tests give flexibility in comparing experimental conditions and can help solve the multiple comparisons problem. By incorporating biophysically motivated constraints, the sensitivity of the statistical test can be greatly improved. The paper is aimed at both neuroscientists looking for data analysis methods and methodologists interested in the theory behind nonparametric tests. The nonparametric test is shown to be formally correct in controlling false alarms under the null hypothesis of identical probability distributions in different experimental conditions.